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Results tagged with at.algebraic-topology
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user 9833
Homotopy theory, homological algebra, algebraic treatments of manifolds.
35
votes
3
answers
1k
views
Incorrect information in an old article about the Kervaire invariant
In the Soviet times there was a famous Encyclopedia of Mathematics. I think it is still familiar to every Russian mathematician maybe except very young ones, and yours truly is in possession …
- 3,526
18
votes
2
answers
1k
views
What is the generator of $\pi_9(S^2)$?
This is more or less the same question as
[ What is the generator of $\pi_9(S^3)$? ], except what I would like to know is if it is possible to describe this map in a way
not only topologists can mak …
- 27.2k
17
votes
Accepted
Does the Gauss-Bonnet theorem apply to non-orientable surfaces?
The answer is already given in the comments (by Ryan Budney and Mizar). But I think it makes sense to clear this confusing point. The classical Gauss-Bonnet formula is [e.g. https://en.wikipedia.or …
- 6,891
4
votes
0
answers
88
views
On decidability of a homeomorphism with a prescribed pushforward
This is a refinement of my older question
A homeomorphism with a prescribed action on the fundamental group - decidable or not?
The problem under considreation is the following. Let $M,N$ be two clo …
- 6,891
9
votes
1
answer
281
views
A homeomorphism with a prescribed action on the fundamental group - decidable or not?
I am curious if the following topological problem is decidable.
Let $M,N$ be two closed manifolds. Given a group isomorphism $p: \pi_1(M)\to \pi_1(N)$, is there a homeomorphism
$\phi: M\to N$ such …
- 6,891
3
votes
0
answers
234
views
Homotopy type of a locally contractible compact
Does a locally contractible compact space have the homotopy type of a finite CW complex? (I think it probably does, but I need a reference anyway.)
EDIT: My intuition was wrong [to see why, read C.T …
- 6,891