All Questions
9 questions
17
votes
1
answer
1k
views
How can gauge theory techniques be useful to study when topological manifolds can be triangulated?
I was reading a review article arXiv:1310.7644 and it was explained there that in the last few years it was proven that there are topological manifolds of dimension greater than four that cannot be ...
- 6,133
13
votes
1
answer
899
views
Critical dimensions D for "smooth manifolds iff triangulable manifolds"
I am aware that at least for lower dimensions,
"smooth manifolds iff triangulable manifolds"
at least for dimensions below a certain critical dimensions D.
My question is that for
For ...
- 10.5k
8
votes
0
answers
170
views
Is there a combinatorial representation of general topological manifolds similar to triangulations?
Piece-wise linear manifolds are combinatorially represented by simplicial complexes modulo Pachner moves. However, for dimensions greater than $3$, the notions of piece-wise linear and topological ...
- 3,001
6
votes
1
answer
708
views
Triangulation of Surfaces without Jordan-Schoenflies
Does anyone know of a proof of the fact that any 2-manifold can be triangulated that does not use the Jordan-Curve Theorem or the Jordan-Schoenflies Theorem? Thanks for your help
- 63
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 ...
- 345
6
votes
0
answers
209
views
If $X_d$ is a non-triangulable manifold, can $X_d \times T^k$, $X_d \times I^k$, or $X_d \times \mathbb{R}^k$ be a triangulable manifold?
If $X_d$ is a non-triangulable manifold, can $X_d \times T^k$, $X_d \times I^k$, or $X_d \times \mathbb{R}^k$ always be a triangulable manifold?
Let $X_d$ be a $d$-manifold which is NOT a ...
- 10.5k
5
votes
2
answers
222
views
$\mathbb{CP}(2)$ from gluing boundary of 4-ball
Many manifolds can be obtained from gluing the boundary of a ball. For example, $\mathbb{RP}(2)$ is obtained from gluing the two edges of a bi-gon (2-ball). Or, lens spaces are obtained from a 3-cell ...
- 3,001
5
votes
1
answer
380
views
existence of triangulations of manifolds
Let $M$ be a smooth manifold.
Let $K$ be a simplicial complex.
Let ${\rm sd}(K)$ be the sub-division of $K$.
Suppose there exists a simplicial sub-complex $K_1$ of ${\rm sd}(K)$ such that $K_1$ ...
- 123
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