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16 votes
1 answer
905 views

Can one determine the dimension of a manifold given its 1-skeleton?

This may be an easy question, but I can't think of the answer at hand. Suppose that I have a triangulated $n$-manifold $M$ (satisfying any set of conditions that you feel like). Suppose that I give ...
Simon Rose's user avatar
  • 6,290
4 votes
1 answer
255 views

Is every (not necessarily PL-) triangulation of a manifold pure, non-branching and strongly-connected?

A triangulation of a topological manifold $\mathcal{M}$ possibly with boundary is an abstract simplicial complex $\Delta$ together with a homeomorphism $\varphi:\vert\Delta\vert\to\mathcal{M}$, where $...
B.Hueber's user avatar
  • 1,171
3 votes
0 answers
221 views

Category of Manifolds and Maps: TOP $\supseteq$ TRI $\supseteq$ PL $\supseteq$ DIFF? [closed]

Please let me denote the following (TOP) topological manifolds https://en.wikipedia.org/wiki/Topological_manifold (PDIFF), for piecewise differentiable https://en.wikipedia.org/wiki/PDIFF (PL) ...
annie marie cœur's user avatar