All Questions
Tagged with gn.general-topology triangulations
9 questions
17
votes
1
answer
582
views
Finite union of closed convex sets is triangulable?
I posted this question on math.stackexchange.com, but didn't get an answer.
Let $A_1, \ldots, A_k \subseteq \mathbb{R}^n$ be closed convex sets. Is the union $\bigcup_{i=1}^k A_i$ triangulable, that ...
- 271
16
votes
1
answer
906
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 ...
- 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 $...
- 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) ...
- 2,147
3
votes
0
answers
102
views
Find a certain triangulation subordinate to a given covering of a manifold
Let $\{U_\alpha\}$ be a covering of a smooth manifold $M$. Replacing it by a refined covering if necessary, we may assume some good properties of it, like, (1) any intersection $\cap_{i=1}^k U_{\...
- 2,789
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 ...
- 781
1
vote
1
answer
135
views
Annulus theorem for pseudomanifolds
Lets say I take an arbitrary closed and smooth $d$-manifolds $\mathcal{M}$. Now, it is a well-known fact that whenever I take two (sufficiently nice embedded) closed $d$-balls $B_{1}$ and $B_{2}$ in $\...
- 1,429
0
votes
1
answer
518
views
Distance between two points using triangulation
Suppose we have two points $p_1$ and $p_2$ in a metric space with unknown dimensionality, with no way to directly compute the distance between them, e.g. no coordinates.
Say we can randomly sample a ...
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 ...
- 781