some inkspace pictures

This commit is contained in:
Maria Marchwicka 2019-06-03 11:18:24 +02:00
parent b9d956bfef
commit 51b13da59c
5 changed files with 399 additions and 1 deletions

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@ -550,8 +550,12 @@ If $K$ is a knot, then $n$ is necessarily even, and so $\Delta_K(t^{-1}) = t^{-n
\end{align*}
\end{lemma}
\begin{proof}
If $\Sigma$ is a genus $g$ - Seifert surface for $K$ then $H_1(\Sigma) = \mathbb{Z}^{2g}$, so $S$ is an $2g \times 2g$ matrix. Therefore $\det (tS - S^T)$ is a polynomial of degree at most $2g$.
\end{proof}
\begin{example}
There are not trivial knots with Alexander polynomial equal $1$, for example:
$\Delta_{11n34} \equiv 1$.
\end{example}
%removing one disk from surface doesn't change $H_1$ (only $H_2$)
\section{}
\begin{example}