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Results tagged with gt.geometric-topology
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user 59302
Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).
7
votes
Accepted
A homeomorphism with a prescribed action on the fundamental group - decidable or not?
This is undecidable. For a construction, see the first page of Nabutovsky and Weinberger, "Algorithmic aspects of homeomorphism problems", Rothenberg Festschrift 1998.
- 934
6
votes
Accepted
Triangulation of a simplex
You are looking for the edgewise subdivision:
Edelsbrunner, H.; Grayson, D. R., Edgewise subdivision of a simplex, Discrete Comput. Geom. 24, No. 4, 707-719 (2000). ZBL0968.51016.
The basic idea is to …
- 934
6
votes
Accepted
Unknotting algorithm in higher dimensions?
The version of the problem in dimensions higher than 4 is undecidable, by work of Nabutovsky and Weinberger:
https://link.springer.com/content/pdf/10.1007/BF02566428.pdf
This is related to the undecid …
- 934
4
votes
Local complexity of triangulations
Here's a stab at a proof that works for non-smoothable manifolds, which seems to be related to Florian Frick's sketch. I'm going to call manifolds with at most $L$ simplices incident to a vertex "of …
- 934
3
votes
A variant of $\ell^2$-cochains
I'm not sure if this should be a comment rather than an answer, since I'm not attempting to answer the hard questions (2) and (3). But it's too long to be a comment. That said:
First of all, I just …
- 934