# Questions tagged [group-cohomology]

In mathematics, group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group representations, group cohomology looks at the group actions of a group G in an associated G-module M to elucidate the properties of the group.

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### Profinite projective and free modules

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### Group extensions with non-abelian kernel

**3**

**1**answer

### Cohomology of commutative monoid acting on module

**6**

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### Top cohomology of profinite Poincaré duality group

**1**

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### Rack cohomology as derived functor cohomology

**6**

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### Galois cohomology with coefficients in the unit group of a cyclotomic field

**3**

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### Group cohomology with coefficients in a graded module

**5**

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### What is known about the discrete group cohomology $H^2(\mathrm{SL}_2(\mathbb C), \mathbb C^\times)$?

**4**

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### Neutral cohomology classes and restriction maps for $H^2$ in group cohomology

**10**

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### A road map through group cohomology

**6**

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### Finite $\Gamma$-modules with trivial $H^2$, where $\Gamma$ is a group of order 2

**11**

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### Constraints on the homology of amenable groups

**5**

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### Using HoTT, why is twisted cohomology of BG group cohomology?

**3**

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### Standard terminology for “observable” subgroups of discrete groups

**6**

**1**answer

### Cohomology of finite $p$-groups over integers in local fields

**6**

**1**answer

### Betti numbers and lower central series quotients of finite-index subgroups of nilpotent groups

**2**

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### Regular conjugacy classes and irreducible representations in the infinite, projective case

**8**

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### A conjecture of Adams on the mod p cohomology of classifying spaces of Lie groups

**7**

**1**answer

### A finitely presented group whose rational cohomology is not nilpotent

**2**

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### Effaceing group cohomology of restricted representations

**16**

**1**answer

### How many cells needed to build the classifying space $BG$?

**5**

**1**answer

### What is the meaning of this coboundary homomorphism for group hypercohomology?

**3**

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### $\ell$-adic cohomology of a quotient by group action

**2**

**1**answer

### A conceptual explanation for a simple fact about twists of objects with abelian automorphism group

**4**

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### Rational cohomology cohomology of $p$-adic analytic groups

**2**

**1**answer

### Non-trivial example of $H^2(G,M)$ where $M$ is a non-trivial G-representation

**5**

**1**answer

### Which groups have undetectable third U(1)-cohomology?

**0**

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### Central extensions of orthogonal group by $C_2$

**2**

**1**answer

### A description of the fundamental class of the group cohomology of the fundamental group of an orientable surface of genus $g$

**2**

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### kernel and cokernel of corestriction map in cohomology of a profinite group

**4**

**1**answer

### Conjugation action on relative homology

**2**

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### Homology $H_{\ast}(T, V)$

**0**

**1**answer

### Second homotopy group of the wedge sum of $S^2$ with the presentation complex of a finitely generated group

**0**

**1**answer

### Computation of the groups $K(BU \times \mathbb{Z})$ and $H^*(BU \times \mathbb{Z})$

**6**

**1**answer

### Are the Galois actions on automorphisms of twists isomorphic?

**5**

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### What is the image of the diagonal map on the cohomology of Lie groups

**4**

**1**answer

### Computing cohomology using bounded hypercovers

**6**

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### Cohomology of the Baer-Specker group

**28**

**2**answers

### Is Lie group cohomology determined by restriction to finite subgroups?

**4**

**1**answer

### Elementary $p$-subgroups of a compact Lie group

**2**

**1**answer

### Find $a$ satisfying $x \cup_1 y = \delta a$ when $x,y \in Z^2(G,\mathbb{Z}_2)$

**5**

**1**answer

### loop space of a finite CW-complex

**3**

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### Colimits in cohomology of profinite arithmetic groups

**3**

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### Rational cohomology of p-adic general linear groups

**20**

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### Which classes in $\mathrm{H}^4(B\mathrm{Exceptional}; \mathbb{Z})$ are classical characteristic classes?

**5**

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### What is $H^1(\mathbb Z, GL_k(R_n))$ for a ring closely related to the cyclotomic rings of integers?

**1**

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### surjective algebra homomorphism $k\widetilde{G} \to k_\alpha G$

**1**

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### What can be said about the Chow rings of classifying spaces of semi-direct products of groups?

**0**

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### When is the natural map of Tate cohomology an isomorphism?

**5**

**2**answers