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6 votes
2 answers
370 views

Does every triangulable manifold have a vertex-transitive triangulation?

Does every triangulable manifold have a vertex-transitive triangulation? When I talk about a vertex-transitive triangulation of a manifold, I mean in the sense of realizing a manifold homeomorphically ...
Mike's user avatar
  • 345
0 votes
1 answer
101 views

A question on relation of different triangulations of a triangulable space

Suppose we get two triangulations of a manifold with boundary $M$ such that the triangulation is compatible with boundary, i.e. the restriction on the boundary is itself a triangulation, is it these ...
Hao Yu's user avatar
  • 781
2 votes
0 answers
138 views

Does any smooth oriented closed orbifold have a fundamental class

This thread:triangulation of orbifolds has shown that any smooth closed orbifold has a triangulation. My further question is: if the difference of any two triangulations $P$ and $Q$ is a boundary of a ...
Hao Yu's user avatar
  • 781
11 votes
2 answers
326 views

Triangulation with simplices of same volume

Let $M$ be a Riemannian smooth compact manifold. It is known that $M$ has a triangulation, for any dimension. But do we know if there exists a triangulation such that all simplices have same volume ? ...
Thibault Lefeuvre's user avatar
10 votes
0 answers
742 views

Can any smooth triangulation of a smooth manifold be blurred?

For the purposes of this question, let's say that a blurring of a smooth triangulation $T$ of a smooth manifold $X$ is a smooth homotopy $h\colon [0,1] \times X \to X$ such that $h_0=\operatorname{id}...
Dmitri Pavlov's user avatar
2 votes
0 answers
104 views

Existence of triangulation of Lipschitz domains

Consider a bounded Lipschitz domain $\Omega \subset \mathbb R^n$. Q1: Can its closure $\overline\Omega$ be triangulated? Q2: If yes, can the triangulation be chosen as finite? Furthermore, how ...
shuhalo's user avatar
  • 5,327