lectures_on_knot_theory/knots_macros.tex

%%%%%%%%%% Oriented LR RM splitting %%%%%%%%%%%%
\newcommand\PICorientLRsplitRM{\setlength{\unitlength}{0.5mm}
\begin{picture}(10,8)(-1.5,2)
%under:
\qbezier(0,0)(1,0.7)(1.5,1.1)
\qbezier(3.4, 2.8)(6,4)(3.4, 5.2)
\qbezier(1.5,6.9)(1,7.3)(0,8)
%over:
\qbezier(6,0)(-3,4)(6,8)
%%%%%%%%%%%%%%%%%%%
\put(-1,9){\vector(-3.5,3){0.2}}%
\put(7,9){\vector(3.3,3){0.2}}
\end{picture}}


\newcommand\PICorientpluscrossRMup{\setlength{\unitlength}{2mm}
\begin{picture}(2.9,2)(-1.4,-0.6)
\put(-1,-1){\vector(1,1){2.3}}%
%%%%%%%%%%%%%%
\put(-1,1){\vector(-1,1){0.3}}%
\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
%%%
%%%
\qbezier(-1.5, 0.2)(-0.8, 0.2)(-0.8,0.3)
\qbezier(-0.35, 0.7)(0, 1.3)(0.35,0.7)
\qbezier(0.8, 0.3)(0.8, 0.2)(1.5,0.2)
\put(1.5,0.2){\vector(1,0){0.3}}%
\end{picture}}
\newcommand\PICorientpluscrossRMdown{\setlength{\unitlength}{2mm}
\begin{picture}(2.9,2)(-1.4,-0.6)
\put(-1,-1){\vector(1,1){2.3}}%
%%%%%%%%%%%%%%
\put(-1,1){\vector(-1,1){0.3}}%
\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
%%%
\qbezier(-1.5, 0.2)(-0.7, 0.2)(-0.6,-0.3)
\qbezier(-0.4, -0.7)(0, -1.3)(0.4,-0.7)
\qbezier(0.6, -0.3)(0.7, 0.2)(1.5,0.2)
\put(1.5,0.2){\vector(1,0){0.3}}%
\end{picture}}

%%%%%%%%%%%%%%
%%%%%% mine %%%%%
%%% Unoriented LR splitting RM move III II solve %%%%%%%%%%%%
\newcommand\PICunorientpluscrossRMsolveDOWN{\setlength{\unitlength}{2.5mm}
\begin{picture}(2.9,1.9)(-1.3,-0.6)
%\qbezier(-1,-1)(0.0,0.0)(1,1)
%%%%%%%%
%\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
%\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
%%%left
\qbezier(-1.2,-1.2)(0.5,0)(-1.2,1.2) 

\qbezier(1.2,-1.2)(-0.5,0)(1.2,1.2)
%%%%%%%%%%%%
\qbezier(-1.5, 0.2)(-0.7, 0.2)(-0.6,-0.3)
\qbezier(-0.4, -0.7)(0, -1.3)(0.4,-0.7)
\qbezier(0.6, -0.3)(0.7, 0.2)(1.5,0.2)
\end{picture}}
%%% Unoriented LR splitting RM move III II solve %%%%%%%%%%%%
\newcommand\PICunorientpluscrossRMsolveUP{\setlength{\unitlength}{2.5mm}
\begin{picture}(2.9,1.9)(-1.3,-0.6)
%\qbezier(-1,-1)(0.0,0.0)(1,1)
%%%%%%%%
%\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
%\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
%%%left
\qbezier(-1.2,-1.2)(0.5,0)(-1.2,1.2) 
%rigth
\qbezier(1.2,-1.2)(-0.5,0)(1.2,1.2)
%%%%%%%%%%%%
\qbezier(-1.5, 0.2)(-0.8, 0.2)(-0.8,0.3)
\qbezier(-0.35, 0.7)(0, 1.3)(0.35,0.7)
\qbezier(0.8, 0.3)(0.8, 0.2)(1.5,0.2)
\end{picture}}
%%%%%%%%%
\newcommand\PICunorientpluscrossRMsolveHorizontalDown{\setlength{\unitlength}{2.5mm}
\begin{picture}(2.9,1.9)(-1.3,-0.6)
%\qbezier(-1,-1)(0.0,0.0)(1,1)
%%%%%%%%
%\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
%\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
%%%left
\qbezier(1.2,1.2)(0,-1)(-1.2,1.2) 
%rigth
\qbezier(-1.2,-1.2)(0,0)(1.2,-1.2)
%%%%%%%%%%%%
\qbezier(-1.5, 0.2)(-0.7, 0.2)(-0.6,-0.3)
\qbezier(-0.4, -0.7)(0, -1.3)(0.4,-0.7)
\qbezier(0.6, -0.3)(0.7, 0.2)(1.5,0.2)
\end{picture}}
%%%%%%%%%%%%%%
\newcommand\PICunorientpluscrossRMsolveHorizontal{\setlength{\unitlength}{2.5mm}
\begin{picture}(2.9,1.9)(-1.3,-0.6)
%\qbezier(-1,-1)(0.0,0.0)(1,1)
%%%%%%%%
%\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
%\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
%%%left
\qbezier(1.2,1.2)(0,-1)(-1.2,1.2) 
%rigth
\qbezier(-1.2,-1.2)(0,0)(1.2,-1.2)
%%%%%%%%%%%%
\qbezier(-1.5, 0.2)(-0.8, 0.2)(-0.8,0.3)
\qbezier(-0.35, 0.7)(0, 1.3)(0.35,0.7)
\qbezier(0.8, 0.3)(0.8, 0.2)(1.5,0.2)
\end{picture}}
\newcommand\PICunorientLRsplitSolve{\setlength{\unitlength}{0.6mm}
\begin{picture}(9,6)(-1,2)
\qbezier(0,0)(1,0.7)(1.5,1.1)
%\qbezier(3.4, 2.8)(6,4)(3.6, 5)
\qbezier(6,8)(3,4)(0,8)
\qbezier(6,0)(-3,6)(4,4)
\qbezier(4,4)(4,2)(4,2)
%\qbezier(6,4)(-3,6)(4,3)
\end{picture}}
%%%%%%%%%%%%%%
%%%%%% mine %%%%%
%%% Unoriented LR splitting RM move II %%%%%%%%%%%%
\newcommand\PICunorientLRsplitRM{\setlength{\unitlength}{0.6mm}
\begin{picture}(9,6)(-1,2)
\qbezier(0,0)(1,0.7)(1.5,1.1)
\qbezier(3.4, 2.8)(6,4)(3.4, 5.2)
\qbezier(1.5,6.9)(1,7.3)(0,8)
\qbezier(6,0)(-3,4)(6,8)
\end{picture}}

\newcommand\PICunorientpluscrossRMup{\setlength{\unitlength}{2.5mm}
\begin{picture}(2.9,1.9)(-1.3,-0.6)
\qbezier(-1,-1)(0.0,0.0)(1,1)
%%%%%%%
\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
%%%
\qbezier(-1.5, 0.2)(-0.8, 0.2)(-0.8,0.3)
\qbezier(-0.35, 0.7)(0, 1.3)(0.35,0.7)
\qbezier(0.8, 0.3)(0.8, 0.2)(1.5,0.2)
\end{picture}}

\newcommand\PICunorientpluscrossRMdown{\setlength{\unitlength}{2.5mm}
\begin{picture}(2.9,1.9)(-1.3,-0.6)
\qbezier(-1,-1)(0.0,0.0)(1,1)
%%%%%%%
\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
%%%
\qbezier(-1.5, 0.2)(-0.7, 0.2)(-0.6,-0.3)
\qbezier(-0.4, -0.7)(0, -1.3)(0.4,-0.7)
\qbezier(0.6, -0.3)(0.7, 0.2)(1.5,0.2)
\end{picture}}


%%%%%% Symbol-Pictures  %%%%%%%%%%%%%%%

% thickness of lines in symbol-pictures
\linethickness{0.3pt}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% UNORIENTED  %%% UNORIENTED %%% UNORIENTED %%% UNORIENTED %%% UNORIENTED  

%%% Unoriented trivial line
\newcommand\PICline{\setlength{\unitlength}{2.5mm}
\begin{picture}(2,1)
\put(0.9,-0.5){\line(0,1){2}}
\end{picture}}

%%% Trivial circle
\newcommand\PICcircle{\setlength{\unitlength}{3mm}
\begin{picture}(1.8,1)(0.2,0.5) 
\put(1,1){\circle{1.2}}
\end{picture}}

%%% Union of unoriented vertical line and circle
\newcommand\PIClinecircle{\setlength{\unitlength}{2.5mm}
\begin{picture}(4.5,1.2)(0.5,0.5)
\put(1,0){\line(0,1){2}} \put(1.7,0.4){\small$\sqcup$}
\put(3.8,1){\circle{1.2}}
\end{picture}}

%%% Unoriented LR splitting %%%%%%%%%%%%
\newcommand\PICunorientLRsplit{\setlength{\unitlength}{0.6mm}
\begin{picture}(9,6)(-1,2)
\qbezier(0,0)(4,4)(0,8) \qbezier(6,0)(2,4)(6,8)
\end{picture}}



%%% Unoriented UD splitting %%%%%%%%%%%%
\newcommand\PICunorientUDsplit{\setlength{\unitlength}{0.6mm}
\begin{picture}(11,6)(-1,1)
\qbezier(0,6)(4,2)(8,6) \qbezier(0,0)(4,4)(8,0)
\end{picture}}

%%%%%%%%%% Unoriented line + crossing %%%%%%%%%%%%
\newcommand\PICunorientpluscross{\setlength{\unitlength}{2mm}
\begin{picture}(2.9,1.9)(-1.3,-0.6)
\qbezier(-1,-1)(0.0,0.0)(1,1)
%%%%%%%
\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
\end{picture}}

%%%%%%%%%% Unoriented line - crossing %%%%%%%%%%%%
\newcommand\PICunorientminuscross{\setlength{\unitlength}{2mm}
\begin{picture}(2.9,1.9)(-1.3,-0.6)
\qbezier(1,-1)(0.0,0.0)(-1,1)
%%%%%%%
\qbezier(0.3,0.3)(0.8,0.8)(1.0,1.0)
\qbezier(-0.3,-0.3)(-0.8,-0.8)(-1.0,-1.0)
\end{picture}}

%%%%%%%%%% Unoriented open writhes gamma_{+} %%%%%%%%%%%%
\newcommand\PICopengammaplus{\setlength{\unitlength}{0.5mm}
\begin{picture}(11,8)(-2,-6)
%top-left Bezier
\qbezier(1.4,-5.2)(2.0,-6.2)(3.2,-6.1)
%top-right Bezier
\qbezier(3.2,-6.2)(6.0,-6.2)(6.2,-3.1)
%bottom-right Bezier
\qbezier(6.2,-3.1)(5.9,-0.3)(3.1,-0)
%bottom-left Bezier
\qbezier(3.1,-0)(0.3,-0.3)(0.0,-2.9)
%line
\put(0.0,-3.1){\line(0,-1){7}} \put(0,0.8){\line(0,1){4}}
\end{picture}}

%%%%%%%%%% Unoriented open writhes gamma_{-} %%%%%%%%%%%%
\newcommand\PICopengammaminus{\setlength{\unitlength}{0.5mm}
\begin{picture}(11,8)(-2,0)
%top-left Bezier
\qbezier(1.4,5.2)(2.0,6.2)(3.2,6.1)
%top-right Bezier
\qbezier(3.2,6.2)(6.0,6.2)(6.2,3.1)
%bottom-right Bezier
\qbezier(6.2,3.1)(5.9,0.3)(3.1,0)
%bottom-left Bezier
\qbezier(3.1,0)(0.3,0.3)(0.0,2.9)
%line
\put(0.0,3.1){\line(0,1){7}} \put(0,-0.8){\line(0,-1){4}}
\end{picture}}

%%%%%%%%%% Unoriented closed writhes gamma_{+} %%%%%%%%%%%%
\newcommand\PICclosedgammaplus{\setlength{\unitlength}{0.5mm}
\begin{picture}(12,7)(-6,-2)

%%%% Right Branch %%%%%%%%%
%Right-bottom-left Bezier
\qbezier(1.4,-2.3)(2.0,-3.3)(3.2,-3.2)
%Right-bottom-right Bezier
\qbezier(3.2,-3.3)(6.0,-3.3)(6.2,-0.3)
%Right-top-right Bezier
\qbezier(6.2,-0.2)(5.9,2.6)(3.1,2.9)
%Right-top-left Bezier
\qbezier(3.1,2.9)(0.3,2.6)(0.0,0.0)

%%%% Left Branch %%%%%%%%%
%Left-bottom-right Bezier
\qbezier(-3.1,-2.9)(-0.3,-2.6)(0.0,0.0)
%Left-bottom-left Bezier
\qbezier(-6.2,0.2)(-5.9,-2.6)(-3.1,-2.9)
%Left-top-left Bezier
\qbezier(-3.2,3.3)(-6.0,3.3)(-6.2,0.3)
%Left-top-right Bezier
\qbezier(-1.4,2.3)(-2.0,3.3)(-3.2,3.2)
\end{picture}}

%%%%%%%%%% Unoriented closed writhes gamma_{-} %%%%%%%%%%%%
\newcommand\PICclosedgammaminus{\setlength{\unitlength}{0.5mm}
\begin{picture}(12,7)(-6,-2)

%%%% Right Branch %%%%%%%%%
%Right-top-left Bezier
\qbezier(1.4,2.3)(2.0,3.3)(3.2,3.2)
%Right-top-right Bezier
\qbezier(3.2,3.3)(6.0,3.3)(6.2,0.3)
%Right-bottom-right Bezier
\qbezier(6.2,0.2)(5.9,-2.6)(3.1,-2.9)
%Right-bottom-left Bezier
\qbezier(3.1,-2.9)(0.3,-2.6)(0.0,0.0)

%%%% Left Branch %%%%%%%%%
%Left-top-right Bezier
\qbezier(-3.1,2.9)(-0.3,2.6)(0.0,0.0)
%Left-top-left Bezier
\qbezier(-6.2,-0.2)(-5.9,2.6)(-3.1,2.9)
%Left-bottom-left Bezier
\qbezier(-3.2,-3.3)(-6.0,-3.3)(-6.2,-0.3)
%Left-bottom-right Bezier
\qbezier(-1.4,-2.3)(-2.0,-3.3)(-3.2,-3.2)
\end{picture}}

%%%%%%%%%% Unoriented close writhes gamma_{+} %%%%%%%%%%%%
\newcommand\PICclosegammaplus{\setlength{\unitlength}{0.5mm}
\begin{picture}(16,8)(-8,-2)
%RIGHT-top-left Bezier
\qbezier(1.4,-1.8)(2.0,-2.7)(3.2,-2.9)
%RIGHT-top-right Bezier
\qbezier(3.2,-2.9)(6.0,-2.7)(6.2,-0.2)
%RIGHT-bottom-right Bezier
\qbezier(6.2,-0.2)(5.9,2.6)(3.1,2.9)
%RIGHT-bottom-left Bezier
\qbezier(3.1,2.9)(0.3,2.6)(0.0,0.0)
%%%%%%
%%%%%%
%LEFT-top-right Bezier
\qbezier(-1.4,1.8)(-2.0,2.7)(-3.2,2.9)
%LEFT-top-left Bezier
\qbezier(-3.2,2.9)(-6.0,2.7)(-6.2,0.2)
%LEFT-bottom-left Bezier
\qbezier(-6.2,0.2)(-5.9,-2.6)(-3.1,-2.9)
%LEFT-bottom-right Bezier
\qbezier(-3.1,-2.9)(-0.3,-2.6)(0.0,0.0)
\end{picture}}

%%%%%%%%%% Unoriented close writhes gamma_{-} %%%%%%%%%%%%
\newcommand\PICclosegammaminus{\setlength{\unitlength}{0.5mm}
\begin{picture}(16,8)(-8,-2)
%RIGHT-top-left Bezier
\qbezier(-1.4,-1.8)(-2.0,-2.7)(-3.2,-2.9)
%RIGHT-top-right Bezier
\qbezier(-3.2,-2.9)(-6.0,-2.7)(-6.2,-0.2)
%RIGHT-bottom-right Bezier
\qbezier(-6.2,-0.2)(-5.9,2.6)(-3.1,2.9)
%RIGHT-bottom-left Bezier
\qbezier(-3.1,2.9)(-0.3,2.6)(0.0,0.0)
%%%%%%
%%%%%%
%LEFT-top-right Bezier
\qbezier(1.4,1.8)(2.0,2.7)(3.2,2.9)
%LEFT-top-left Bezier
\qbezier(3.2,2.9)(6.0,2.7)(6.2,0.2)
%LEFT-bottom-left Bezier
\qbezier(6.2,0.2)(5.9,-2.6)(3.1,-2.9)
%LEFT-bottom-right Bezier
\qbezier(3.1,-2.9)(0.3,-2.6)(0.0,0.0)
\end{picture}}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% ORIENTED  %%% ORIENTED %%% ORIENTED %%% ORIENTED %%% ORIENTED %%% ORIENTED 

%%%%%%%%%% Oriented trivial line %%%%%%%%%%%%
\newcommand\PICorientline{\setlength{\unitlength}{2.5mm}
\begin{picture}(2,1)
\put(0.9,-0.5){\vector(0,1){2}}
\end{picture}}

%%%%%%%%%% Oriented trivial circle -- right  %%%%%%%%%%
\newcommand\PICorientcircleright{\setlength{\unitlength}{3mm}
\begin{picture}(1.8,1)(0.2,0.5) \put(1,1){\circle{1.2}}
\put(1.3,1.55){\vector(1,0){0.01}}   %%% Put arrow to the circle
\end{picture}}

%%%%%%%%%% Oriented trivial circle -- left  %%%%%%%%%%
\newcommand\PICorientcircleleft{\setlength{\unitlength}{3mm}
\begin{picture}(1.8,1)(0.2,0.5) \put(1,1){\circle{1.2}}
 \put(0.7,1.55){\vector(-1,0){0.01}}   %%% Put arrow to the circle
\end{picture}}

%%% Union of oriented vertical line and circle
\newcommand\PICorientlinecircle{\setlength{\unitlength}{2.5mm}
%\begin{picture}(3.5,1.2)(0.5,0.5)
%\put(1,0){\vector(0,1){2}} \put(1.7,0.4){\small$\sqcup$}
%\put(2.6,1){\circle{1.2}}
%\end{picture}}
\begin{picture}(3.2,1.2)(0.5,0.5)
\put(1,0){\vector(0,1){2}}
\put(2.6,1){\circle{1.2}}
\end{picture}}

%%% Union of oriented vertical line and oriented circle right
\newcommand\PICorientlinecircler{\setlength{\unitlength}{2.5mm}
%\begin{picture}(3.5,1.2)(0.5,0.5)
%\put(1,0){\vector(0,1){2}} \put(1.7,0.4){\small$\sqcup$}
%\put(2.6,1){\circle{1.2}}
%\end{picture}}
\begin{picture}(3.2,1.2)(0.5,0.5)
\put(1,0){\vector(0,1){2}}
\put(2.6,1){\circle{1.2}}
\put(2.9,1.6){\vector(1,0){0.01}}
\end{picture}}

%%%%%%%%%% Oriented line + crossing %%%%%%%%%%%%
\newcommand\PICorientpluscross{\setlength{\unitlength}{2mm}
\begin{picture}(2.9,2)(-1.4,-0.6)
\put(-1,-1){\vector(1,1){2.3}}%
%%%%%%%%%%%%%%
\put(-1,1){\vector(-1,1){0.3}}%
\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
\end{picture}}

%%%%%%%%%% Oriented line - crossing %%%%%%%%%%%%
\newcommand\PICorientminuscross{\setlength{\unitlength}{2mm}
\begin{picture}(2.9,2)(-1.4,-0.6)
\put(1,-1){\vector(-1,1){2.3}}%
%%%
\put(1,1){\vector(1,1){0.3}}%
\qbezier(0.3,0.3)(0.8,0.8)(1.0,1.0)
\qbezier(-0.3,-0.3)(-0.8,-0.8)(-1.0,-1.0)
\end{picture}}

%%%%%%%%%% Oriented LR splitting %%%%%%%%%%%%
\newcommand\PICorientLRsplit{\setlength{\unitlength}{0.5mm}
\begin{picture}(10,8)(-1.5,2)
%\arc
\qbezier(0,0)(4,4)(0,8)
%%%%%%%%%%%%%%%%%%%
\qbezier(6,0)(2,4)(6,8)
%%%%%%%%%%%%%%%%%%%
\put(-0.2,9){\vector(-2,3){0.2}}%
\put(7,9){\vector(2,3){0.2}}
\end{picture}}

%%% Oriented UD splitting %%%%%%%%%%%%
\newcommand\PICorientUDsplit{\setlength{\unitlength}{0.6mm}
\begin{picture}(11,6)(-1,1)
\qbezier(0,6)(4,2)(8,6)
\qbezier(0,0)(4,4)(8,0)
%%%%%%%%%%%%%%%%%%%
\put(-0.4,6.2){\vector(-3,2){0.2}}%
\put(8.4,6.2){\vector(3,2){0.2}}
\put(-0.4,-0.2){\vector(-3,-2){0.2}}%
\put(8.4,-0.2){\vector(3,-2){0.2}}
\end{picture}}

%%%%%%%%%% Oriented open writhes gamma_{+} %%%%%%%%%%%%
\newcommand\PICorientopengammaplus{\setlength{\unitlength}{0.5mm}
\begin{picture}(12,8)(-2.5,-6)
%top-left Bezier
\qbezier(1.4,-5.2)(2.0,-6.2)(3.2,-6.1)
%top-right Bezier
\qbezier(3.2,-6.2)(6.0,-6.2)(6.2,-3.1)
%bottom-right Bezier
\qbezier(6.2,-3.1)(5.9,-0.3)(3.1,-0)
%bottom-left Bezier
\qbezier(3.1,-0)(0.3,-0.3)(0.0,-2.9)
%line
\put(0.0,-3.1){\line(0,-1){7}} \put(0,0.8){\vector(0,1){4}}
\end{picture}}

%%%%%%%%%% Oriented open writhes gamma_{-} %%%%%%%%%%%%
\newcommand\PICorientopengammaminus{\setlength{\unitlength}{0.5mm}
\begin{picture}(12,8)(-2.5,0)
%top-left Bezier
\qbezier(1.4,5.2)(2.0,6.2)(3.2,6.1)
%top-right Bezier
\qbezier(3.2,6.2)(6.0,6.2)(6.2,3.1)
%bottom-right Bezier
\qbezier(6.2,3.1)(5.9,0.3)(3.1,0)
%bottom-left Bezier
\qbezier(3.1,0)(0.3,0.3)(0.0,2.9)
%line
\put(0.0,3.1){\vector(0,1){7}} \put(0,-0.8){\line(0,-1){4}}
\end{picture}}

%%%%%%%%%% Oriented clockwise overcurve %%%%%%%%%%%%
\newcommand\PICorientclockwise{\setlength{\unitlength}{0.6mm}
\begin{picture}(11,6)(-1,1)
\qbezier(0,3)(4,7)(8,3) \put(8,3){\vector(3,-2){0.1}}
\end{picture}}

%%%%%%%%%% Oriented anti-clockwise undercurve %%%%%%%%%%%%
\newcommand\PICorientanticlockwise{\setlength{\unitlength}{0.6mm}
\begin{picture}(11,6)(-1,1)
\qbezier(0,3)(4,-1)(8,3) \put(8,3){\vector(3,2){0.1}}
\end{picture}}

%%%%%%%%%% Oriented anti-clockwise overcurve %%%%%%%%%%%%
\newcommand\PICorientanticlockwiseover{\setlength{\unitlength}{0.6mm}
\begin{picture}(11,6)(-1,1)
\qbezier(0,3)(4,7)(8,3) \put(0,3){\vector(-3,-2){0.1}}
\end{picture}}

%%%%%%%%%% Oriented closed writhes gamma_{+} %%%%%%%%%%%%
\newcommand\PICorientclosedgammaplus{\setlength{\unitlength}{0.5mm}
\begin{picture}(12,7)(-6,-2)

%%%% Right Branch %%%%%%%%%
%Right-bottom-left Bezier
\qbezier(1.4,-2.3)(2.0,-3.3)(3.2,-3.2)
%Right-bottom-right Bezier
\qbezier(3.2,-3.3)(6.0,-3.3)(6.2,-0.3)
%Right-top-right Bezier
\qbezier(6.2,-0.2)(5.9,2.6)(3.1,2.9)
%Right-top-left Bezier
\qbezier(3.1,2.9)(0.3,2.6)(0.0,0.0)
 \put(4.7,2.7){\vector(3,0){0.05}}     %%% Putting arrow to \gamma+
% \put(-4.9,3.2){\vector(-3,0){0.04}}

%%%% Left Branch %%%%%%%%%
%Left-bottom-right Bezier
\qbezier(-3.1,-2.9)(-0.3,-2.6)(0.0,0.0)
%Left-bottom-left Bezier
\qbezier(-6.2,0.2)(-5.9,-2.6)(-3.1,-2.9)
%Left-top-left Bezier
\qbezier(-3.2,3.3)(-6.0,3.3)(-6.2,0.3)
%Left-top-right Bezier
\qbezier(-1.4,2.3)(-2.0,3.3)(-3.2,3.2)
\end{picture}}

%%%%%%%%%% Oriented closed writhes gamma_{-} %%%%%%%%%%%%
\newcommand\PICorientclosedgammaminus{\setlength{\unitlength}{0.5mm}
\begin{picture}(12,7)(-6,-2)

%%%% Right Branch %%%%%%%%%
%Right-top-left Bezier
\qbezier(1.4,2.3)(2.0,3.3)(3.2,3.2)
%Right-top-right Bezier
\qbezier(3.2,3.3)(6.0,3.3)(6.2,0.3)
%Right-bottom-right Bezier
\qbezier(6.2,0.2)(5.9,-2.6)(3.1,-2.9)
%Right-bottom-left Bezier
\qbezier(3.1,-2.9)(0.3,-2.6)(0.0,0.0)
% \put(4.9,3.2){\vector(3,0){0.04}}     %%% Putting arrow to \gamma-
 \put(-4.7,2.7){\vector(-3,0){0.05}}

%%%% Left Branch %%%%%%%%%
%Left-top-right Bezier
\qbezier(-3.1,2.9)(-0.3,2.6)(0.0,0.0)
%Left-top-left Bezier
\qbezier(-6.2,-0.2)(-5.9,2.6)(-3.1,2.9)
%Left-bottom-left Bezier
\qbezier(-3.2,-3.3)(-6.0,-3.3)(-6.2,-0.3)
%Left-bottom-right Bezier
\qbezier(-1.4,-2.3)(-2.0,-3.3)(-3.2,-3.2)
\end{picture}}

%%%%%%%%%% RibbonUnknot %%%%%%%%%%%%
\newcommand\PICRibbonUnknot{\setlength{\unitlength}{0.5mm}
\begin{picture}(12,8)(-2.5,0)
\put(-2,-2.4){\includegraphics[width=0.035\textwidth]{RibbonUnknot}}
\end{picture}}

%%%%%%%%%% TwistedUnknot %%%%%%%%%%%%
\newcommand\PICTwistedUnknot{\setlength{\unitlength}{0.5mm}
\begin{picture}(12,8)(-2.5,0)
\put(-2,-2.4){\includegraphics[width=0.035\textwidth]{TwistedUnknot}}
\end{picture}}

%%%%%%%%%% Dehn surgery_{+} %%%%%%%%%%%%
\newcommand\PICDehnplus{\setlength{\unitlength}{0.5mm}
\begin{picture}(12,8)(-2.5,0)
\put(-2,-2.4){\includegraphics[width=0.1\textwidth]{Twplus}}
\end{picture}}

%%%%%%%%%% Dehn surgery_{-} %%%%%%%%%%%%
\newcommand\PICDehnminus{\setlength{\unitlength}{0.5mm}
\begin{picture}(12,8)(-2.5,0)
\put(-3,-2){\includegraphics[width=0.1\textwidth]{Twminus}}
\end{picture}}

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