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Results tagged with at.algebraic-topology
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user 4760
Homotopy theory, homological algebra, algebraic treatments of manifolds.
9
votes
4
answers
2k
views
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
16
votes
2
answers
2k
views
Can anyone explain to me what is an assembly map?
Or can you give me a good place to read about things related to assembly map, besides wikipedia? I am specially interested in the case of algebraic K-theory. Would appreciated if you could provide exa …
- 1,598
9
votes
Why torsion is important in (co)homology ?
Integer Pontrjagin classes are diffeomorphism invariant, while rational Pontrjagin classes are homeomorphism invariant, due to Novikov. Also there are examples where two smooth manifolds are homeomor …
16
votes
2
answers
2k
views
Smooth structures on the connected sum of a manifold with an Exotic sphere
What can we say about the connected sum of a manifold $M^n$ with an Exotic sphere? Is is possible some of them are still diffemorphic to $M^n$. Is it possible to classifying all the exotic smooth stru …
- 1,598
16
votes
1
answer
5k
views
Is it true that all real projective space $RP^n$ can not be smoothly embedded in $R^{n+1}$ f...
So first for n even, $RP^n$ is not orientable, hence can not be embedded in $\mathbb{R}^{n+1}$.
For odd n, $RP^{n}$ is orientable, hence the normal bundle is trivial. Now using stiefel-Whitney classe …
- 1,598