diff --git a/images/ball_4.pdf b/images/ball_4.pdf index b624733..2a42527 100644 Binary files a/images/ball_4.pdf and b/images/ball_4.pdf differ diff --git a/images/ball_4.pdf_tex b/images/ball_4.pdf_tex index 88b0b2f..2c7105b 100644 --- a/images/ball_4.pdf_tex +++ b/images/ball_4.pdf_tex @@ -36,7 +36,7 @@ }% \providecommand\rotatebox[2]{#2}% \ifx\svgwidth\undefined% - \setlength{\unitlength}{640.00045656bp}% + \setlength{\unitlength}{618.60012745bp}% \ifx\svgscale\undefined% \relax% \else% @@ -48,17 +48,18 @@ \global\let\svgwidth\undefined% \global\let\svgscale\undefined% \makeatother% - \begin{picture}(1,0.33301347)% + \begin{picture}(1,0.34188524)% \put(0,0){\includegraphics[width=\unitlength,page=1]{ball_4.pdf}}% - \put(0.09657807,0.16873207){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{1.7204386\unitlength}\raggedright $B^4$\end{minipage}}}% + \put(0.09991916,0.17192056){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{1.7799568\unitlength}\raggedright $B^4$\end{minipage}}}% \put(0,0){\includegraphics[width=\unitlength,page=2]{ball_4.pdf}}% - \put(0.43862137,0.2802709){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.15019764\unitlength}\raggedright \end{minipage}}}% - \put(0.35652029,0.19426923){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.17633501\unitlength}\raggedright $\Sigma$\end{minipage}}}% - \put(0.56151038,0.2638857){\color[rgb]{0,0,0}\makebox(0,0)[lb]{\smash{ }}}% + \put(0.45379538,0.28731805){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.1553937\unitlength}\raggedright \end{minipage}}}% + \put(0.36885404,0.19834118){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.18243528\unitlength}\raggedright $\Sigma$\end{minipage}}}% + \put(0.58093571,0.27036601){\color[rgb]{0,0,0}\makebox(0,0)[lb]{\smash{ }}}% \put(0,0){\includegraphics[width=\unitlength,page=3]{ball_4.pdf}}% - \put(0.60849603,0.17781348){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{1.72442485\unitlength}\raggedright $B^4$ \end{minipage}}}% + \put(0.60835677,0.18396491){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{1.78408096\unitlength}\raggedright $B^4$ \end{minipage}}}% \put(0,0){\includegraphics[width=\unitlength,page=4]{ball_4.pdf}}% - \put(0.88514345,0.20410866){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.17633501\unitlength}\raggedright $\widetilde{\Sigma}$\end{minipage}}}% + \put(0.74492,0.13965334){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.18243528\unitlength}\raggedright $\widetilde{\Sigma}$\end{minipage}}}% \put(0,0){\includegraphics[width=\unitlength,page=5]{ball_4.pdf}}% + \put(0.89860534,0.20628745){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.18243528\unitlength}\raggedright $\Sigma$\end{minipage}}}% \end{picture}% \endgroup% diff --git a/images/ball_4.svg b/images/ball_4.svg index 8ff1677..dc7a74e 100644 --- a/images/ball_4.svg +++ b/images/ball_4.svg @@ -10,9 +10,9 @@ xmlns="http://www.w3.org/2000/svg" xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd" xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape" - width="126.77666mm" - height="154.37773mm" - viewBox="0 0 449.20862 547.00771" + width="218.22838mm" + height="74.609062mm" + viewBox="0 0 773.25015 264.36282" id="svg2" version="1.1" inkscape:version="0.92.2 5c3e80d, 2017-08-06" @@ -649,13 +649,13 @@ borderopacity="1.0" inkscape:pageopacity="0.0" inkscape:pageshadow="2" - inkscape:zoom="0.45772981" - inkscape:cx="160.35988" - inkscape:cy="481.62781" + inkscape:zoom="0.91545962" + inkscape:cx="365.17503" + inkscape:cy="5.3643255" inkscape:document-units="px" inkscape:current-layer="layer1" showgrid="false" - inkscape:window-width="1388" + inkscape:window-width="1395" inkscape:window-height="855" inkscape:window-x="0" inkscape:window-y="1" @@ -685,34 +685,6 @@ transform="translate(-184.35289,-66.379889)"> - - $B^4$    - $\widetilde{\Sigma}$ + + + + + $B^4$  + $\widetilde{\Sigma}$ + $\Sigma$ + + diff --git a/images/ball_4_alpha_beta.pdf b/images/ball_4_alpha_beta.pdf new file mode 100644 index 0000000..6fb97f3 Binary files /dev/null and b/images/ball_4_alpha_beta.pdf differ diff --git a/images/ball_4_alpha_beta.pdf_tex b/images/ball_4_alpha_beta.pdf_tex new file mode 100644 index 0000000..6611460 --- /dev/null +++ b/images/ball_4_alpha_beta.pdf_tex @@ -0,0 +1,62 @@ +%% Creator: Inkscape inkscape 0.92.2, www.inkscape.org +%% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 +%% Accompanies image file 'ball_4_alpha_beta.pdf' (pdf, eps, ps) +%% +%% To include the image in your LaTeX document, write +%% \input{.pdf_tex} +%% instead of +%% \includegraphics{.pdf} +%% To scale the image, write +%% \def\svgwidth{} +%% \input{.pdf_tex} +%% instead of +%% \includegraphics[width=]{.pdf} +%% +%% Images with a different path to the parent latex file can +%% be accessed with the `import' package (which may need to be +%% installed) using +%% \usepackage{import} +%% in the preamble, and then including the image with +%% \import{}{.pdf_tex} +%% Alternatively, one can specify +%% \graphicspath{{/}} +%% +%% For more information, please see info/svg-inkscape on CTAN: +%% http://tug.ctan.org/tex-archive/info/svg-inkscape +%% +\begingroup% + \makeatletter% + \providecommand\color[2][]{% + \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% + \renewcommand\color[2][]{}% + }% + \providecommand\transparent[1]{% + \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% + \renewcommand\transparent[1]{}% + }% + \providecommand\rotatebox[2]{#2}% + \ifx\svgwidth\undefined% + \setlength{\unitlength}{269.33681939bp}% + \ifx\svgscale\undefined% + \relax% + \else% + \setlength{\unitlength}{\unitlength * \real{\svgscale}}% + \fi% + \else% + \setlength{\unitlength}{\svgwidth}% + \fi% + \global\let\svgwidth\undefined% + \global\let\svgscale\undefined% + \makeatother% + \begin{picture}(1,0.78365053)% + \put(0,0){\includegraphics[width=\unitlength,page=1]{ball_4_alpha_beta.pdf}}% + \put(0.07129767,0.41643827){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{4.09759322\unitlength}\raggedright $\Omega$ \end{minipage}}}% + \put(0,0){\includegraphics[width=\unitlength,page=2]{ball_4_alpha_beta.pdf}}% + \put(1.03643632,1.49942703){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.35690094\unitlength}\raggedright \end{minipage}}}% + \put(0.86250743,0.48500479){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.41900878\unitlength}\raggedright $\alpha$\end{minipage}}}% + \put(0,0){\includegraphics[width=\unitlength,page=3]{ball_4_alpha_beta.pdf}}% + \put(0.70129363,0.75268051){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.41900878\unitlength}\raggedright $\beta$\end{minipage}}}% + \put(0.51878746,0.6158009){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.41900878\unitlength}\raggedright $B$\end{minipage}}}% + \put(0.65870887,0.39679348){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.41900878\unitlength}\raggedright $A$\end{minipage}}}% + \end{picture}% +\endgroup% diff --git a/images/ball_4_alpha_beta.svg b/images/ball_4_alpha_beta.svg new file mode 100644 index 0000000..c765a8a --- /dev/null +++ b/images/ball_4_alpha_beta.svg @@ -0,0 +1,838 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + + + $\Omega$  + $\Sigma$ $\alpha$ + + + + + + + $\beta$ $B$ $A$ + diff --git a/images/ball_4_branched.svg b/images/ball_4_branched.svg new file mode 100644 index 0000000..875dd1c --- /dev/null +++ b/images/ball_4_branched.svg @@ -0,0 +1,1752 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + + + $B^4\setminus \Sigma$  + $\Sigma$ $\Sigma$ $\widetilde{\Sigma}$ + $\Sigma$ + + + + + + + + + + + + + + + pusched cycle $\alpha$ + diff --git a/images/ball_4_pushed_cycle.pdf b/images/ball_4_pushed_cycle.pdf new file mode 100644 index 0000000..502c74a Binary files /dev/null and b/images/ball_4_pushed_cycle.pdf differ diff --git a/images/ball_4_pushed_cycle.pdf_tex b/images/ball_4_pushed_cycle.pdf_tex new file mode 100644 index 0000000..f63f508 --- /dev/null +++ b/images/ball_4_pushed_cycle.pdf_tex @@ -0,0 +1,65 @@ +%% Creator: Inkscape inkscape 0.92.2, www.inkscape.org +%% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 +%% Accompanies image file 'ball_4_pushed_cycle.pdf' (pdf, eps, ps) +%% +%% To include the image in your LaTeX document, write +%% \input{.pdf_tex} +%% instead of +%% \includegraphics{.pdf} +%% To scale the image, write +%% \def\svgwidth{} +%% \input{.pdf_tex} +%% instead of +%% \includegraphics[width=]{.pdf} +%% +%% Images with a different path to the parent latex file can +%% be accessed with the `import' package (which may need to be +%% installed) using +%% \usepackage{import} +%% in the preamble, and then including the image with +%% \import{}{.pdf_tex} +%% Alternatively, one can specify +%% \graphicspath{{/}} +%% +%% For more information, please see info/svg-inkscape on CTAN: +%% http://tug.ctan.org/tex-archive/info/svg-inkscape +%% +\begingroup% + \makeatletter% + \providecommand\color[2][]{% + \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% + \renewcommand\color[2][]{}% + }% + \providecommand\transparent[1]{% + \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% + \renewcommand\transparent[1]{}% + }% + \providecommand\rotatebox[2]{#2}% + \ifx\svgwidth\undefined% + \setlength{\unitlength}{347.08935595bp}% + \ifx\svgscale\undefined% + \relax% + \else% + \setlength{\unitlength}{\unitlength * \real{\svgscale}}% + \fi% + \else% + \setlength{\unitlength}{\svgwidth}% + \fi% + \global\let\svgwidth\undefined% + \global\let\svgscale\undefined% + \makeatother% + \begin{picture}(1,0.60810254)% + \put(0,0){\includegraphics[width=\unitlength,page=1]{ball_4_pushed_cycle.pdf}}% + \put(0.15918243,0.32787147){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{3.17967897\unitlength}\raggedright $B^4$ \end{minipage}}}% + \put(0,0){\includegraphics[width=\unitlength,page=2]{ball_4_pushed_cycle.pdf}}% + \put(0.80426108,1.16353579){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.27695048\unitlength}\raggedright \end{minipage}}}% + \put(0.60504575,0.51512601){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.32514535\unitlength}\raggedright $\Sigma$\end{minipage}}}% + \put(0.43509938,0.46211893){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.32514535\unitlength}\raggedright $\widetilde{\Sigma}$\end{minipage}}}% + \put(0,0){\includegraphics[width=\unitlength,page=3]{ball_4_pushed_cycle.pdf}}% + \put(0.86395261,1.02736704){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.27695048\unitlength}\raggedright \end{minipage}}}% + \put(0,0){\includegraphics[width=\unitlength,page=4]{ball_4_pushed_cycle.pdf}}% + \put(0.50926006,0.0219968){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.34368681\unitlength}\raggedright pusched cycle $\alpha$\end{minipage}}}% + \put(0,0){\includegraphics[width=\unitlength,page=5]{ball_4_pushed_cycle.pdf}}% + \put(0.81107494,0.33205799){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.34368681\unitlength}\raggedright cycle $\alpha$\end{minipage}}}% + \end{picture}% +\endgroup% diff --git a/images/ball_4_pushed_cycle.svg b/images/ball_4_pushed_cycle.svg new file mode 100644 index 0000000..b726fd4 --- /dev/null +++ b/images/ball_4_pushed_cycle.svg @@ -0,0 +1,1768 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 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\global\let\svgwidth\undefined% \global\let\svgscale\undefined% \makeatother% - \begin{picture}(1,0.32391422)% + \begin{picture}(1,0.36183256)% + \put(0.27511336,0.95541378){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.27931736\unitlength}\raggedright \end{minipage}}}% + \put(1.79035789,1.29094878){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{1.05568767\unitlength}\raggedright \end{minipage}}}% \put(0,0){\includegraphics[width=\unitlength,page=1]{covering.pdf}}% - \put(0.36517261,0.14344765){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.08173531\unitlength}\raggedright $S_0$\end{minipage}}}% - \put(0.50092807,0.14212963){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.08173531\unitlength}\raggedright $N_0$\end{minipage}}}% - \put(0.63800154,0.13685758){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.08173531\unitlength}\raggedright $S_1$\end{minipage}}}% - \put(0.77902906,0.14081162){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.08173531\unitlength}\raggedright $N_1$\end{minipage}}}% - \put(0.20437487,0.14312235){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.08173531\unitlength}\raggedright $N_{-1}$\end{minipage}}}% + \put(0.375672,0.17131524){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.08408535\unitlength}\raggedright $S_0$\end{minipage}}}% + \put(0.51533068,0.16995933){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.08408535\unitlength}\raggedright $N_0$\end{minipage}}}% + \put(0.65634526,0.16453569){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.08408535\unitlength}\raggedright $S_1$\end{minipage}}}% + \put(0.80142758,0.16860343){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.08408535\unitlength}\raggedright $N_1$\end{minipage}}}% + \put(0.21025104,0.17098059){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.08408535\unitlength}\raggedright $N_{-1}$\end{minipage}}}% \put(0,0){\includegraphics[width=\unitlength,page=2]{covering.pdf}}% - \put(0.26355737,0.06317987){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.20429219\unitlength}\raggedright $a_0, a_1, a_2, \cdots, a_n$\end{minipage}}}% - \put(0.25437673,0.36322151){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.27151093\unitlength}\raggedright \end{minipage}}}% - \put(1.72727281,0.68937889){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{1.02618304\unitlength}\raggedright \end{minipage}}}% - \put(0.33843921,0.32554504){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.3217213\unitlength}\raggedright $\alpha_0, \alpha_1, \alpha_2, \cdots, \alpha_n$\end{minipage}}}% - \put(0.6458685,0.05813393){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.20429219\unitlength}\raggedright $ta_0, ta_1, ta_2, \cdots, ta_n$\end{minipage}}}% - \put(0.33178373,0.36960419){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.2255384\unitlength}\raggedright \end{minipage}}}% - \put(0.01309653,0.2920601){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.35886479\unitlength}\raggedright $t^{-1}a_0, t^{-1}a_1, t^{-1}a_2, \cdots, t^{-1}a_n$\end{minipage}}}% - \put(0.66929097,0.32088516){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.38416371\unitlength}\raggedright $t\alpha_0, t\alpha_1, t\alpha_2, \cdots, t\alpha_n$\end{minipage}}}% + \put(0.06101596,0.07198974){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.18711552\unitlength}\raggedright \shortstack{$ t^{-1}\alpha_1, t^{-1}\alpha_2, \cdots, t^{-1}\alpha_n$}\end{minipage}}}% + \put(0.56677018,0.35673072){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.30643553\unitlength}\raggedright \shortstack{$ta_1, ta_2, \cdots, ta_n$}\end{minipage}}}% + \put(0.28338509,0.3553748){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.21016596\unitlength}\raggedright $a_1, a_2, \cdots, a_n$\end{minipage}}}% + \put(0.27524963,0.02317699){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.21016596\unitlength}\raggedright $a_j$\end{minipage}}}% + \put(0.41626421,0.02317699){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.21016596\unitlength}\raggedright $a_i^+$\end{minipage}}}% \put(0,0){\includegraphics[width=\unitlength,page=3]{covering.pdf}}% - \put(0.16216395,0.01462151){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.10438141\unitlength}\raggedright $a_j^{-}$\\ \end{minipage}}}% - \put(0.50047151,0.04817267){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.10438141\unitlength}\raggedright $a_i^{+}$\\ \end{minipage}}}% + \put(0.48541563,0.07605746){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.37829873\unitlength}\raggedright \shortstack{$\alpha_1, \alpha_2, \cdots, \alpha_n$}\end{minipage}}}% + \put(0,0){\includegraphics[width=\unitlength,page=4]{covering.pdf}}% \end{picture}% \endgroup% diff --git a/images/covering.svg b/images/covering.svg index a4935ae..ff952bc 100644 --- a/images/covering.svg +++ b/images/covering.svg @@ -9,9 +9,9 @@ xmlns="http://www.w3.org/2000/svg" xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd" xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape" - width="144.9989mm" - height="10.536824mm" - viewBox="0 0 144.9989 10.536824" + width="788.45831mm" + height="285.28989mm" + viewBox="0 0 788.45832 285.28988" version="1.1" id="svg3201" inkscape:version="0.92.2 5c3e80d, 2017-08-06" @@ -65,22 +65,6 @@ id="path3045" inkscape:connector-curvature="0" /> - - - + transform="translate(631.78479,-394.31526)"> + + - - - - $S_0$ $S_1$ $N_{-1}$ - - - + id="path1382" + d="M 156.67351,457.26191 H 44.03661 c 0.0187,16.62453 -2.50171,34.02418 -1.44006,50.62548 6.4177,2.37532 15.66471,-0.49121 22.31862,0.12056 84.89735,-68.68308 38.93013,91.05728 6.03166,15.56405 -7.91276,-2.62837 -29.25395,-2.94134 -26.91022,8.56876 v 40.0259 h 112.6369" + style="opacity:1;fill:none;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:3;stroke-linejoin:bevel;stroke-miterlimit:4;stroke-dasharray:3, 3;stroke-dashoffset:0;stroke-opacity:1" /> + + + $a_0, a_1, a_2, \cdots, a_n$ $a_0, a_1, a_2, \cdots, a_n$ \shortstack{$ t^{-1}\alpha_1, t^{-1}\alpha_2, \cdots, t^{-1}\alpha_n$} $a_0, a_1, a_2, \cdots, a_n$ \shortstack{$ta_1, ta_2, \cdots, ta_n$} $a_1, a_2, \cdots, a_n$ $a_j$ $a_0, a_1, a_2, \cdots, a_n$ + id="flowPara14570">$a_i^+$ + \shortstack{$\alpha_1, \alpha_2, \cdots, \alpha_n$} + diff --git a/images/knot_complement.pdf b/images/knot_complement.pdf new file mode 100644 index 0000000..e5d1571 Binary files /dev/null and b/images/knot_complement.pdf differ diff --git a/images/knot_complement.pdf_tex b/images/knot_complement.pdf_tex new file mode 100644 index 0000000..9f52c0c --- /dev/null +++ b/images/knot_complement.pdf_tex @@ -0,0 +1,66 @@ +%% Creator: Inkscape inkscape 0.92.2, www.inkscape.org +%% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 +%% Accompanies image file 'knot_complement.pdf' (pdf, eps, ps) +%% +%% To include the image in your LaTeX document, write +%% \input{.pdf_tex} +%% instead of +%% \includegraphics{.pdf} +%% To scale the image, write +%% \def\svgwidth{} +%% \input{.pdf_tex} +%% instead of +%% \includegraphics[width=]{.pdf} +%% +%% Images with a different path to the parent latex file can +%% be accessed with the `import' package (which may need to be +%% installed) using +%% \usepackage{import} +%% in the preamble, and then including the image with +%% \import{}{.pdf_tex} +%% Alternatively, one can specify +%% \graphicspath{{/}} +%% +%% For more information, please see info/svg-inkscape on CTAN: +%% http://tug.ctan.org/tex-archive/info/svg-inkscape +%% +\begingroup% + \makeatletter% + \providecommand\color[2][]{% + \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% + \renewcommand\color[2][]{}% + }% + \providecommand\transparent[1]{% + \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% + \renewcommand\transparent[1]{}% + }% + \providecommand\rotatebox[2]{#2}% + \ifx\svgwidth\undefined% + \setlength{\unitlength}{1725.07393424bp}% + \ifx\svgscale\undefined% + \relax% + \else% + \setlength{\unitlength}{\unitlength * \real{\svgscale}}% + \fi% + \else% + \setlength{\unitlength}{\svgwidth}% + \fi% + \global\let\svgwidth\undefined% + \global\let\svgscale\undefined% + \makeatother% + \begin{picture}(1,0.66258733)% + \put(0,0){\includegraphics[width=\unitlength,page=1]{knot_complement.pdf}}% + \put(-0.01227477,0.64110885){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.36188263\unitlength}\raggedright \end{minipage}}}% + \put(1.95087091,1.07582686){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{1.36774537\unitlength}\raggedright \end{minipage}}}% + \put(0,0){\includegraphics[width=\unitlength,page=2]{knot_complement.pdf}}% + \put(0.64135944,0.10337544){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.48923401\unitlength}\raggedright \shortstack{$\Lk(\alpha_j, a_i) = \delta_ij$}\end{minipage}}}% + \put(0.71869386,0.2853112){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.30566784\unitlength}\raggedright \shortstack{$a_1, \cdots, a_n$ - generators of $H_1(S)$}\end{minipage}}}% + \put(0,0){\includegraphics[width=\unitlength,page=3]{knot_complement.pdf}}% + \put(0.22299352,0.32899579){\color[rgb]{1,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.085914\unitlength}\raggedright $K$\end{minipage}}}% + \put(0.3165171,0.48250877){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.10894069\unitlength}\raggedright $N$\end{minipage}}}% + \put(0.48505125,0.66476096){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.39877356\unitlength}\raggedright \shortstack{$\alpha_1, \cdots, \alpha_n$ - dual generators of $H_1(N)$}\end{minipage}}}% + \put(0.789951,0.31913458){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.10894069\unitlength}\raggedright $S$\end{minipage}}}% + \put(0.30627525,0.40285468){\color[rgb]{1,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.1131259\unitlength}\raggedright \shortstack{$\Sigma \times (-1, 1)$}\end{minipage}}}% + \put(0.31005963,0.22222407){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\begin{minipage}{0.0219589\unitlength}\raggedright \end{minipage}}}% + \end{picture}% +\endgroup% diff --git a/images/knot_complement.svg b/images/knot_complement.svg new file mode 100644 index 0000000..198912b --- /dev/null +++ b/images/knot_complement.svg @@ -0,0 +1,349 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + + + + + \shortstack{$\Lk(\alpha_j, a_i) = \delta_ij$} \shortstack{$a_1, \cdots, a_n$ - generators of $H_1(S)$} + + + + + $K$ $N$ \shortstack{$\alpha_1, \cdots, \alpha_n$ - dual generators of $H_1(N)$} $S$ \shortstack{$\Sigma \times (-1, 1)$} + diff --git a/lectures_on_knot_theory.pdf b/lectures_on_knot_theory.pdf index ce66041..ff7884a 100644 Binary files a/lectures_on_knot_theory.pdf and b/lectures_on_knot_theory.pdf differ