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55 questions
5
votes
0
answers
155
views
Low dimensional homotopy fibration TOP(M) -> TOP(int(M))
In the thesis of Nancy Cardim she proves that for $M$ a topological manifold of dim $\geq 5$ with connected boundary, there exists a homotopy fiber sequence
$C(\partial M)\rightarrow TOP(M) \...
- 93
33
votes
1
answer
1k
views
Nilpotence of the stable Hopf map via framed cobordism
The Pontryagin-Thom construction shows that the stable homotopy groups of spheres are the same as the groups of stably framed manifolds up to cobordism. Specifically the Hopf map corresponds to the ...
CommunityBot
- 1
10
votes
2
answers
757
views
Embedded (framed) cobordisms
[The title initially was "Actions of gauge groups on framed cobordisms. This has been changed.]
This question is a follow-up to my answer to When is a submanifold of $\mathbf R^n$ given by global ...
CommunityBot
- 1
4
votes
1
answer
291
views
Lower dimensional Pin cobordisms
I'm studying Pin cobordism groups of a point for some low dimensions. I found a general result by Anderson, Brown, Peterson in Theorem 5.1 of their paper "Pin cobordism and related topics" http://...
- 3,051
2
votes
0
answers
430
views
The signature of a mapping torus
Consider a manifold $M$ of dimension $4k + 2$, $k$ an integer. Pick a diffeomorphism $\phi$ of $M$ and construct the mapping torus $T$ of $\phi$. Suppose that there is a $4k+4$ dimensional manifold $B$...
- 1,582