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Results tagged with cohomology
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user 5323
A branch of algebraic topology concerning the study of cocycles and coboundaries. It is in some sense a dual theory to homology theory. This tag can be further specialized by using it in conjunction with the tags group-cohomology, etale-cohomology, sheaf-cohomology, galois-cohomology, lie-algebra-cohomology, motivic-cohomology, equivariant-cohomology, ...
9
votes
3
answers
625
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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 topological … That is, given an explicit line bundle $L$ how does one construct an explicit group extension $E$ such that the two give the same cohomology class and vice versa? …
- 2,283
13
votes
4
answers
2k
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Why does (Ribbon) Graph (co)Homology Compute (co)Homology of MCG?
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. …
- 2,283
2
votes
1
answer
1k
views
Penner's formula for volume of the Moduli Space
In his paper "Weil-Petersson Volumes" Penner gives the following formula for the integral of a top-dimensional cohomology class $\omega$ on the moduli space $\mathcal M_g^s$ of $s$-punctured riemann surfaces … 2) Is this formula the ``shadow'' of a general formula for evaluating cohomology classes on (smooth) orbifolds? …
- 2,283