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Results tagged with gt.geometric-topology
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user 4760
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).
9
votes
4
answers
2k
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How to prove the connected sum of two closed aspherical n-manfolds (n >2) is not asperical?
The intuitive idea is that the sphere connected the two manifolds is not contractible, which implies the (n-1)th homotopy group is not zero. Another argument, which I am not totally understand, uses t …
- 1,598
3
votes
0
answers
104
views
Geometric automorphism of free group respect to nonorientable suface
An outer automorphism $[ϕ]\in Out(F_n)$ is geometric if it is induced by a surface homeomorphism h:M→M, where M is a compact surface with nonempty boundary. I am wondering is it enough we only conside …
- 1,598
4
votes
2
answers
471
views
Does a homeomorphism of $S^1 \times S^2$ which is homotopy to the identity has to isotope to...
I guess the question can be asked for all manifolds. But I am particularly interested in $S^1 \times S^2$ right now. Concrete example preferrd.
- 1,598
10
votes
1
answer
1k
views
CAT(0) groups that does not act on CAT(0) cubical complex
CAT(0) groups are groups that act on a CAT(0) space properly and cocompactly. If a group acts on a CAT(0) cubical complex properly and cocompactly, then of course it is a CAT(0) Group. I am wondering …
- 1,598