memoire-m2

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -16,7 +16,7 @@ proof.
   Any closed connected orientable surface is homeomorphic to the connected sum
   \(\Sigma_g\) of the sphere \(\mathbb{S}^2\) with \(g \ge 0\) copies of the
   torus \(\mathbb{T}^2 = \mfrac{\mathbb{R}^2}{\mathbb{Z}^2}\). Any compact
-  connected orientable surface \(\Sigma\) is isomorphic to the surface
+  connected orientable surface \(\Sigma\) is homeomorphic to the surface
   \(\Sigma_g^b\) obtained from \(\Sigma_g\) by removing \(b \ge 0\) open disks
   with disjoint closures.
 \end{theorem}
@@ -136,8 +136,7 @@ of the dissertation at hand.
   The \emph{mapping class group \(\Mod(\Sigma)\) of an orientable surface
   \(\Sigma\)} is the group of isotopy classes of orientation-preserving
   homeomorphisms \(\Sigma \isoto \Sigma\), where both the homeomorphisms and
-  the isotopies are assumed to fix the points of \(\partial \Sigma\) and the
-  punctures of \(\Sigma\).
+  the isotopies are assumed to fix \(\partial \Sigma\) pointwise.
   \[
     \Mod(\Sigma) = \mfrac{\Homeo^+(\Sigma, \partial \Sigma)}{\simeq}
   \]

diff --git a/sections/presentation.tex b/sections/presentation.tex
@@ -201,7 +201,7 @@ get\dots
   \centering
   \includegraphics[width=.4\linewidth]{images/braid-group-center.eps}
   \captionof{figure}{The clockwise rotation by $\sfrac{2\pi}{n}$ about an axis
-  center around the punctures $x_1, \ldots, x_n$ of $\Sigma_{0, n}^1$.}
+  centered around the punctures $x_1, \ldots, x_n$ of $\Sigma_{0, n}^1$.}
   \label{fig:braid-group-center}
 \end{minipage}
 \smallskip