diff --git a/images/11n34.png b/images/11n34.png
new file mode 100644
index 0000000..123e67d
Binary files /dev/null and b/images/11n34.png differ
diff --git a/images/11n34.svg b/images/11n34.svg
new file mode 100644
index 0000000..51a3751
--- /dev/null
+++ b/images/11n34.svg
@@ -0,0 +1,135 @@
+
+
+
+
diff --git a/images/11n34.svg.2019_06_03_08_08_16.0.svg b/images/11n34.svg.2019_06_03_08_08_16.0.svg
new file mode 100644
index 0000000..8567cb2
--- /dev/null
+++ b/images/11n34.svg.2019_06_03_08_08_16.0.svg
@@ -0,0 +1,125 @@
+
+
+
+
diff --git a/images/11n34_v2.svg b/images/11n34_v2.svg
new file mode 100644
index 0000000..6eb4990
--- /dev/null
+++ b/images/11n34_v2.svg
@@ -0,0 +1,134 @@
+
+
+
+
diff --git a/lectures_on_knot_theory.tex b/lectures_on_knot_theory.tex
index 99b6955..773992e 100644
--- a/lectures_on_knot_theory.tex
+++ b/lectures_on_knot_theory.tex
@@ -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}