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-...

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### Cohomology of $\mathbb Z_4$ via the Lyndon-Hochschild-Serre spectral sequence

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### Direct limit of complexes from cocycle property up to homotopy

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### What is the interpretation of the Gerstenhaber bracket?

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### Convolution of sheaves on R

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### Computing $H^*(BDiff(W_{\infty},D^{\infty});\mathbb{Q})$ via Mumford-Morita-Miller classes

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### Why is the Chern Number Invariant under A Continuously Shrinking of the Structure Group?

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### Cohomology of the Hilbert square of a degree 14 K3 surface [Beauville-Donagi]

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### Twisted Chern-Simons, and Twisted Wess-Zumino Term

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### cohomology of flag variety

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### How do we compute the even cohomology $H^{2i}(Q)$ of the affine hyperquadric?

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### $\partial \overline{\partial}$-lemma for Irreducible, Normal Projective Varieties

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### Compute the rational cohomology ring $H^*(M;\mathbb{Q})$ of a product of Lie groups (and their quotients)

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### Poincare duality spaces vs. manifolds via lifting maps, the obstruction theory and the role of simply connectedness

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### Show that the rational cohomology ring $H^*(M;\mathbb{Q})$ needs at least two generators

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### Restricting projective representations of Lie groups to lattices

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### Trivial cohomology with free module coefficient

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### cohomology of the orbit space of a compact totally disconnected group action on a paracompact space

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### A cohomology associated to a symplectic manifold

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### What is closed homology?

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### Relative cohomology in algebraic topology vs algebraic geometry

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### “Rotated” version of the Atiyah-Hirzebruch spectral sequence

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### Cohomology with compact support

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### Kähler form on complex projective algebraic variety [closed]

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### Morava $E$-theory source of reading

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### Milnor's proof of cohomology of BO(n)

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### How to show the equality of two descriptions for the cohomology of a non-finite group

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### Fibre restriction and Leray–Hirsch

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### Extending Beauville-Bogomolov orthogonal decomposition from variety to scheme

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### (pro)Étale cohomology of adic spaces and inverse limit

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### Hochschild homology of a category of modules over an algebra

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### Integral cohomology on compact irreducible holomorphic symplectic manifolds

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### Projective surfaces with vanishing first cohomology

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### Explicit elements of the first cohomology of modular curves

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### Torsion in the integral cohomology of $BPU_{n}$

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### Cup products in the Mayer-Vietoris sequence

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### Why Use Hypercohomology When Defining the de Rham Cohomology of a Smooth Scheme over $k$?

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### finiteness of syntomic cohomology of proper varieties over algebraically closed and finite fields

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### étale vs syntomic vs flat cohomology

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### A cohomology associated to a Riemannian manifold

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### Minakshisundaram-Pleijel zeta function identity

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### Which compact (finite dimensional) Lie groups have $H^1_{DR}(G)\neq 0$

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### Pull back group cohomology onto handle decomposition

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### What is known about the cohomology of the matrix monoid?

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### Description of Koszul dual of Sklyanin algebras

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### Cap product for (co)homology from handle decompositions/Kirby diagrams

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### Cohomology of $ko,tmf,MSpin,MString$ with coefficients $\mathbb{Z}/p$ for odd primes $p$

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### Linear sections of $Gr(V,2)$

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### What is the scope of validity of Kunneth formula for de Rham?

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### Finding generators of equivariant cohomology

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