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Results tagged with gt.geometric-topology
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user 21684
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).
50
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4
answers
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To which extent can one recover a manifold from its group of homeomorphisms
Question. Suppose that $M$ is a closed connected topological manifold and $G$ is its group of homeomorphisms (with compact-open topology). Does $G$ (as a topological group) uniquely determine $M$?
One …
- 31.2k
35
votes
2
answers
4k
views
Good covers of manifolds
It is well-known and easy to prove (see for instance this post) that every smooth manifold admits a good cover, i.e., a locally finite cover by open balls such that all nonempty intersections of the …
- 31.2k
31
votes
1
answer
1k
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Open immersions of open manifolds
For concreteness, I will work in the category of smooth manifolds, but my question makes sense in topological and PL category as well. Recall that a manifold $M$ is called open if every connected comp …
- 31.2k
29
votes
2
answers
3k
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Simple discrete subgroups of Lie groups
Upon Ian Agol's suggestion, I separated this question from the one on non-residual finiteness in
Non-residually finite matrix groups
Question. Are there infinitely generated simple discrete subgrou …
- 31.2k
22
votes
4
answers
2k
views
fixed point property for maps of compacts
Definition. A topological space $X$ has the Fixed Point Property (FPP) if every continuous self-map $X\to X$ has a fixed point.
Question. If $X$ and $Y$ are homotopy-equivalent compact metrizable sp …
- 31.2k
12
votes
1
answer
504
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Tverberg's theorem in CAT(0) spaces
Does Tverberg's theorem hold for CAT(0) spaces of covering dimension $d<\infty$:
Is it true that for any $d$-dimensional $CAT(0)$-space $X$ and a subset $E\subset X$ of cardinality $(d + 1)(r - 1) …
- 31.2k
10
votes
2
answers
535
views
Is there an analogue of Mostow-Palais equivariant embedding theorem for noncompact groups
Let $M$ be a (Hausdorff) smooth compact manifold and $G$ a Lie group acting smoothly on $M$. If $G$ is compact then, by Mostow-Palais theorem, there exists an equivariant smooth embedding $M\to {\mat …
- 31.2k
8
votes
1
answer
380
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embeddings of graphs into surfaces
There is a vast literature on embeddings of graphs into surfaces.
I am interested in embeddings of graphs that
belong to the given homotopy class. Here is the precise formulation.
I have two finit …
- 31.2k