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Results tagged with at.algebraic-topology
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user 16877
Homotopy theory, homological algebra, algebraic treatments of manifolds.
2
votes
1
answer
371
views
Chern numbers of primitive classes in BU
How does one compute Chern numbers of spherical rational homology classes
$$f: S ^{2k} \to BU.$$ These generate rational homology by Milnor-Moore theorem since BU is a connected H-space, and so $c_k$ …
- 491
6
votes
1
answer
1k
views
On Brown representability theorem
The classical Brown representability theorem is for set valued functors. Is there a version for abelian group valued functors, and ring valued functors?
In other words say we have an abelian group v …
- 491
2
votes
0
answers
359
views
Novikov conjecture
The statement of the Novikov conjecture is a bit esoteric. Does the following simplified conjecture have any known counterexamples?
C: For a smooth closed 4n-fold $M$, the Pontryagin numbers are homo …
- 491
5
votes
1
answer
241
views
Is the smooth singular simplicial set of a smooth manifold a Kan complex?
It is classical that the singular simplicial set of a topological space is a Kan complex. This is elementary and already due to presumably Kan.
Q: Is the smooth singular simplicial set of a smooth man …
- 491
3
votes
1
answer
197
views
Does the group of compactly supported diffeomorphisms have the homotopy type of a CW complex?
It is known that the group of diffeomorphisms of a compact manifold with the natural $C^{\infty}$ topology has the homotopy type of a countable CW complex. See for instance this thread: Is the space o …
- 491