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Results tagged with cohomology
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user 161009
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, ...
6
votes
1
answer
353
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Comparing Hochschild (co)homology for algebras and coalgebras
Given a field $k$, an associative $k$-algebra $A$, and an $A$-bimodule $M$, one can define as the Hochschild homology and cohomology as the homology of the complexes
$$M\otimes A^{\otimes n}$$
and
$$\text …
- 518
5
votes
1
answer
252
views
Operadic cohomology in terms of infinitesimal composition
Given a non symmetric operad $\mathcal{O}$, is there an explicit description of its (André-Quillen or other) cohomology in low degrees in terms of infinitesimal composition? … I ask because I am interested in a collection parametrised by objects that are 2-cocycles in the Hochschild cohomology of the following algebra with coefficients in an appropriate bimodule. …
- 518
4
votes
1
answer
397
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Reference for isomorphism between group cohomology and singular cohomology
It is a fairly standard result that
$$ H^i(G, L) \cong H^i(X,\mathcal{L})$$
where the left hand side is the group cohomology and the right hand side is sheaf cohomology. …
- 518
2
votes
Comparing Hochschild (co)homology for algebras and coalgebras
Denote by $HH_n$ and $CH_n$ the Hochschild homology of an algebra and a coalgebra respectively, and similarly for cohomology. …
- 518