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Results tagged with gt.geometric-topology
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user 58307
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).
3
votes
3
answers
249
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Reference for an easy lemma on homeomorphisms of connected manifolds
If M is a connected manifold of dimension $\geq 2$ then the set of orientation preserving homeomorphisms of M that are isotopic to the identity acts $n$-transitively on M for all positive $n\in\mathbb …
- 1,517
34
votes
1
answer
965
views
Classifiying sphere eversions
For a year I have been giving lectures on a (probalby) new way to present an explicit sphere eversion. These lectures include a review of many other explicit eversions that have been described, as tex …
- 1,517
13
votes
1
answer
607
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Fundamental group of the space of immersions of the 2-sphere in 3-space modulo diffeomorphis...
In a previous Mathoverflow question, we saw that the fundamental group of the space $Imm(S^2,\mathbb{R}^3)$ of immersions the 2-sphere in ordinary 3-space is isomorphic to $\mathbb{Z}/2 \times \mathbb …
- 1,517
11
votes
Eversion of the 6-sphere in 7-space
(That's my first post on mathoverflow. Henceforth and unfortunately I am not allowed to post comments (this needs reputation 50), so part of the present post in the answer box would better fit in the …
- 1,517
4
votes
Group of surface homeomorphisms is locally path-connected
In the particular case of surfaces, I found the following reference which includes a proof that is not too complicated: Regular Mappings and the Space of Homeomorphisms on 2-Manifolds by Hamstrom and …
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10
votes
2
answers
431
views
Group of surface homeomorphisms is locally path-connected
I think the following is true and I need a reference for the proof. (Given a closed surface $S$, i.e. a compact 2-dimensional topological manifold (without boundary), we endow $S$ with a distance gene …
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