\begin{lemma}[Milnor Singular Points of Complex Hypersurfaces] \end{lemma} %\end{comment} \noindent An oriented knot is called negative amphichiral if the mirror image $m(K)$ of $K$ is equivalent the reverse knot of $K$: $K^r$. \\ \begin{problem} Prove that if $K$ is negative amphichiral, then $K \# K = 0$ in $\mathscr{C}$. % %\\ %Hint: $ -K = m(K)^r = (K^r)^r = K$ \end{problem} \begin{example} Figure 8 knot is negative amphichiral. \end{example} % % \begin{theorem} Let $H_p$ be a $p$ - torsion part of $H$. There exists an orthogonal decomposition of $H_p$: \[ H_p = H_{p, 1} \oplus \dots \oplus H_{p, r_p}. \] $H_{p, i}$ is a cyclic module: \[ H_{p, i} = \quot{\mathbb{Z}[t, t^{-1}]}{p^{k_i} \mathbb{Z} [t, t^{-1}]} \] \end{theorem} \noindent The proof is the same as over $\mathbb{Z}$. \noindent %Add NotePrintSaveCiteYour opinionEmailShare %Saveliev, Nikolai %Lectures on the Topology of 3-Manifolds %An Introduction to the Casson Invariant \begin{figure}[h] \fontsize{10}{10}\selectfont \centering{ \def\svgwidth{\linewidth} \resizebox{0.5\textwidth}{!}{\input{images/ball_4_alpha_beta.pdf_tex}} } %\caption{Sketch for Fact %%\label{fig:concordance_m} \end{figure}