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juso.koc 2025-03-21 14:09:48 +00:00 committed by node
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prerequisites.tex
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\begin{frame}{Quotients of the $3$-sphere} \begin{frame}{Quotients of the $3$-sphere}
\begin{itemize} \begin{itemize}
\item $\so 4$ is isomorphic to the isometry group of $\S^3$. \item The group $\so 4$ is isomorphic to the isometry group of $\S^3$.
\item Subgroups $\Gamma \leqslant \so 4$ define \textcolor{darkyellow}{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 Subgroups $\Gamma \leqslant \so 4$ define \textcolor{darkyellow}{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 $M \in \Gamma$.
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\item The obtain space is (\emph{sometimes}) a manifold. In particular, it is well defined and spherical for finite $\Gamma$. \item The obtain space is (\emph{sometimes}) a manifold. In particular, it is well defined and spherical for finite $\Gamma$.