diff --git a/main.pdf b/main.pdf index 168b5be..6bad4a9 100644 Binary files a/main.pdf and b/main.pdf differ diff --git a/prerequisites.tex b/prerequisites.tex index 55e4b5e..566cacc 100644 --- a/prerequisites.tex +++ b/prerequisites.tex @@ -19,7 +19,7 @@ \begin{frame}{Quotients of the $3$-sphere} \begin{itemize} \item $\so 4$ is isomorphic to the isometry group of $\S^3$. - \item Subgroups $\Gamma \leqslant \so 4$ define equivalence classes of orbits on $\S^3$ by the standard action of $\so 4$ on $\R^3$, i.e. $x \sim y$ iff $x = My$ for some $M \in \Gamma$. + \item Subgroups $\Gamma \leqslant \so 4$ define equivalence classes of orbits on $\S^3$ by the standard action of $\so 4$ on $\R^4$, i.e. $x \sim y$ iff $x = My$ for some $M \in \Gamma$. \item The obtain space is (\emph{sometimes}) a manifold. In particular, it is well defined and spherical for finite $\Gamma$. \item This can be easily generalised to the $n$-sphere. \end{itemize}