# Questions tagged [cohomology]

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, ...

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### Alexander duality for Homology sphere which is the Geometric realization of a finite simplicial complex

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### Steenrod operations from the delooping viewpoint

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### Why the scissor relations in Grothendieck rings?

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### Cohomology and higher structures

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### Ideals generated by regular sequences

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### Commutative square up to sign as indicated, Poincare duality

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### Effective semi-group of a singular abelian surface

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### Generators for unitary bordism ring $\pi_*(MU)$

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### Models for computing cohomology of Lie groupoids

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### Reference for equivariant derived Künneth formula

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### Understanding top Cech cohomology

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### Signature of a non-compact manifold

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### Beilinson regulator: a road map

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### De Rham and Koszul complexes

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### About the cohomology of $BG^\delta$. Making a Lie group discrete

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### Clarify formula for Steifel-Whitney (Poincaré dual) homology classes in a barycentric subdivision?

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### Integration on an non-orientable manifold [closed]

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### The homology of the universal covering space, why so difficult to compute

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### How to identify cup product with intersection

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### Homological and homotopical equivalence of complex analytic varieties

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### mod $p$ homology of Thom spectra MSU

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### Middle cohomology of very general hyperplane sections

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### Derived category of singular varieties

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### Compact $G$-ENR's and Euler characteristic computed with Alexander-Spanier cohomology with compact support

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### When homology isomorphism implies homotopy isomorphism

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### Stalks of perverse cohomology sheaves?

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### Weyl map for $SU(n)$

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### Find torsion classes using flat bundles

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### Motivating the coefficient field of $\ell$-adic cohomology

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### Homologically trivial fibre

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### Chern classes of complex vector bundle

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### Alexander duality and homology equivalence

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### When is $\mathcal{D}(\mathcal{F}):\mathcal{D}(\mathcal{A})\to \mathcal{D}(\mathcal{B})$ fully faithful?

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### Integral cohomology of compact Lie groups and their classifying spaces

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### $X$ with $H^*(X)=$affine Verma module?

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### Chromatic Homotopy Theory and Physics

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### Category of spaces/sheaves

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### Compactly supported cohomology of a topological DM stack

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### Imperfect Tate (cup product) pairing in Galois cohomology?

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### An intuitive explanation for group cohomology via cochains?

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### Pushforward in Compactly Supported Cohomology

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### 3rd Cohomology of a fibration with Flag varieties as fibers

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### cohomology of curves

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### An action of the symmetric group $S_n$ on group cohomology $H^n(G, A)$ of abelian groups

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### Computation of mod p homology of $MSU$

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### Unifying “cohomology groups classify extensions” theorems

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### A question about Johnson's theorem on the first and second cohomology of commutative amenable algebras

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### $d^3$ in the Atiyah-Hirzebruch spectral sequence for (twisted) $KO$

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### Cohomology of (complex) varieties

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