Titles
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main.tex
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main.tex
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\section{Conclusion}
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\begin{frame}{Conclusion}
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\pause
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\begin{enumerate}
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\item We can infer the shape of the universe from its spectrum.
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\end{frame}
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\begin{frame}{References 2 --- electric boogaloo}
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\begin{frame}{References 2 --- Electric Boogaloo}
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\begin{itemize}
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\item [6] N. Jarosik et. al. \textit{Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Sky Maps, Systematic Errors, and Basic Results}. The American Astronomical Society, 2011.
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\end{itemize}
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\end{frame}
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\begin{frame}{References 3 --- the references strike again}
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\begin{frame}{References 3 --- the References Strike Again}
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\begin{itemize}
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\item [11] E. A. Lauret and B. Linowitz. \textit{The spectral geometry of hyperbolic and spherical manifolds: analogies and open problems}. New York Journal of Mathematics, 2025.
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\item [12] R. Lehoucq, J. Weeks, J. P. Uzan, E. Gausmann, and J.P. Luminet. \textit{Eigenmodes of three-dimensional spherical spaces and their application to cosmology}. Classical and Quantum Gravity, 2002.
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\section{Prerequisites}
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\begin{frame}{Manifolds \& Homotopy groups}
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\begin{frame}{Manifolds \& Homotopy Groups}
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\begin{figure}[H]
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\centering
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\includegraphics[width=0.5\linewidth]{mug-neighbourhoods.png}
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\end{itemize}
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\end{frame}
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\begin{frame}{Lens spaces}
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\begin{frame}{Lens Spaces}
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\begin{itemize}
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\item Lens spaces are obtained by taking the quotient of some $n$-sphere by a cyclic group.
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\item They cannot be distinguished by their homotopy group alone.
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\end{itemize}
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\end{frame}
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\begin{frame}{Lens spaces — the explicit construction}
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\begin{frame}{Lens Spaces — the Explicit Construction}
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\begin{definition}[Lens space]
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Given $q \in \mathbb Z$ and $s \in \mathbb Z ^n$ elementwise coprime with $q$
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\begin{align*}
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