diff --git a/src/ga/06manifolds.tex b/src/ga/06manifolds.tex
index c1d728f..bc67da5 100644
--- a/src/ga/06manifolds.tex
+++ b/src/ga/06manifolds.tex
@@ -1,7 +1,7 @@
 \subsection{Topological manifolds}
 
 \bd
-A paracompact, Hausdorff, topological space $(M,\cO)$ is called a \emph{$d$-dimensional (topological) manifold}\index{manifold}\index{manifold!topological} if for every point $p\in M$ there exist a neighbourhood $U(p)$ and a homeomorphism $x\cl U(p) \to x(U(p)) \se \R^d$. We also write $\dim M = d$.
+A paracompact, Hausdorff, topological space $(M,\cO)$ is called a \emph{$d$-dimensional (topological) manifold}\index{manifold}\index{manifold!topological} if for every point $p\in M$ there exists an open neighbourhood $U(p)$ and a homeomorphism $x\cl U(p) \to x(U(p)) \se \R^d$. We also write $\dim M = d$.
 \ed
 
 Intuitively, a $d$-dimensional\index{dimension!manifold} manifold is a topological space which locally (i.e.\ around each point) looks like $\R^d$. Note that, strictly speaking, what we have just defined are \emph{real} topological manifolds. We could define \emph{complex} topological manifolds as well, simply by requiring that the map $x$ be a homeomorphism onto an open subset of $\C^d$. 
@@ -44,7 +44,7 @@ \subsection{Topological manifolds}
 
 \subsection{Bundles}
 
-Products are very useful. Very often in physics one intuitively thinks of the product of two manifolds as attaching a copy of the second manifold to each point of the first.  However, not all interesting manifolds can be understood as products of manifolds. A classic example of this is the \emph{M\"obius strip}\index{M\"obius strip}.\footnote{The TikZ code for the M\"obius strip was written by \href{http://pgfplots.net/tikz/examples/author/jake/}{Jake} on \href{https://tex.stackexchange.com/questions/118563/moebius-strip-using-tikz}{TeX.SE}.}
+Product manifolds are very useful. Very often in physics one intuitively thinks of the product of two manifolds as attaching a copy of the second manifold to each point of the first.  However, not all interesting manifolds can be understood as products of manifolds. A classic example of this is the \emph{M\"obius strip}\index{M\"obius strip}.\footnote{The TikZ code for the M\"obius strip was written by \href{http://pgfplots.net/tikz/examples/author/jake/}{Jake} on \href{https://tex.stackexchange.com/questions/118563/moebius-strip-using-tikz}{TeX.SE}.}
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