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Results tagged with at.algebraic-topology
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user 5323
Homotopy theory, homological algebra, algebraic treatments of manifolds.
48
votes
3
answers
13k
views
When is a Homology Class Represented by a Submanifold? [duplicate]
Possible Duplicate:
Cohomology and fundamental classes
Given an oriented manifold $M$ and an oriented submanifold $\phi:N\to M$ we can obtain a homology class $\phi_*[N]\in H_*(M) …
- 2,283
23
votes
2
answers
2k
views
Massey Products vs. $A_\infty$-Structures
Does anyone know a good reference for a proof of the fact that given a dga $A$, an $A_\infty$-structure on $HA$ is ''the same'' as coherent choices for all of the higher Massey products of $HA$? More …
- 2,283
13
votes
4
answers
2k
views
Why does (Ribbon) Graph (co)Homology Compute (co)Homology of MCG?
The title says it all. I am looking for an explanation or reference for why the homology of the ribbon graph complex computes the cohomology of the mapping class groups of surfaces.
I've seen explan …
- 2,283
9
votes
3
answers
625
views
Group Extensions and Line Bundles on $BG$
I am sure the answer to this question is well-known, but
It is well known that the group cohomology $H^2(G,\mathbb Z)$ classifies group extensions $0\to \mathbb Z\to E\to G\to 1$ and that for a topo …
- 2,283