memoire-m2

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -60,7 +60,7 @@ example\dots
   Figure~\ref{fig:change-of-coordinates}, each corresponding to one of the
   curves \(\alpha\) and \(\alpha'\) in \(\Sigma\). By identifying the pairs of
   arcs corresponding to the same curve we obtain the surface
-  \(\mfrac{\Sigma_{\alpha \alpha'}}{\sim} \cong S\).
+  \(\mfrac{\Sigma_{\alpha \alpha'}}{\sim} \cong \Sigma\).
 
   Similarly, \(\Sigma_{\beta \beta'} \cong \Sigma_{g-1, r}^{p+1}\) also has an
   additional boundary component \(\delta' \subset \partial \Sigma_{\beta
@@ -69,7 +69,7 @@ example\dots
   \alpha'} \isoto \Sigma_{\beta \beta'}\). Even more so, we can choose
   \(\tilde\phi\) taking each one of the arcs in \(\delta\) to the corresponding
   arc in \(\delta'\). Now \(\tilde\phi\) descends to a self-homeomorphism
-  \(\phi\) the quotient surface \(S \cong \mfrac{\Sigma_{\alpha \alpha'}}{\sim}
+  \(\phi\) the quotient surface \(\Sigma \cong\mfrac{\Sigma_{\alpha \alpha'}}{\sim}
   \cong \mfrac{\Sigma_{\beta \beta'}}{\sim}\). Moreover, \(\phi\) is such that
   \(\phi(\alpha) = \alpha'\) and \(\phi(\beta) = \beta'\), as desired.
 \end{proof}