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Results tagged with cohomology
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user 3377
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, ...
4
votes
Accepted
Cohomology of invariant differential forms
For higher cohomology I think there are some examples. …
- 9,237
2
votes
Holomorphic vector fields acting on Dolbeault cohomology
Klemyatin, Dolbeault cohomology of compact complex manifolds with an action of a complex Lie group, J. Geom. Phys. 157 (2020), 103823.) … Examples when the action is non-trivial are given by Akhiezer in this paper:
Akhiezer, Dmitri
Group actions on the Dolbeault cohomology of homogeneous manifolds.
Math. Z. 226 (1997), no. 4, 607–621. …
- 9,237
8
votes
Hodge dual of de Rham cohomology and singular cohomology
The Hodge * operator action on cohomology is generally speaking
metric-dependent, hence * is not well-defined without fixing the metric.
There are some caveats. … On compact 2n-dimensional manifolds,
the *-operator in the middle cohomology is determined by
the conformal structure. …
- 9,237
6
votes
Accepted
Are the Kahler Identities for a Holomorphic Vector Bundle Actually Interesting?
This commutator happens to be positive or negative when the bundle is positive or negative; vanishing of cohomology follows immediately, because the Laplacians themselves are positive operators. …
- 9,237