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5 votes

Does every triangulable manifold have a vertex-transitive triangulation?

This is to supplement Ian's answer and get examples in all dimensions $\ge 3$. Let $M={\mathbb H}^n/\Gamma$ be a compact hyperbolic $n$-manifold; suppose that $f\in Homeo(M)$ is a homeomorphism of ...
Misha's user avatar
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5 votes

Does every triangulable manifold have a vertex-transitive triangulation?

There exists many closed connected hyperbolic 3-manifolds $M$ with trivial symmetry group, and hence trivial mapping class group. $M$ cannot be homeomorphic to a simplicial complex $\tau$ which admits ...
Ian Agol's user avatar
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9 votes
Accepted

Abstract simplicial complexes - Reference for an elementary definition of mapping degree for simplicial maps?

I think the right generality to restrict to is the following: Let $n$ be a positive integer, and let $X$ and $Y$ be $n$-dimensional oriented simplicial complexes, with the following properties: Every ...
Achim Krause's user avatar
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