# Cohomology of Groups

@inproceedings{Brown1982CohomologyOG, title={Cohomology of Groups}, author={Kenneth S. Brown}, year={1982} }

This advanced textbook introduces students to cohomology theory. No knowledge of homological algebra is assumed beyond what is normally taught in a first course in algebraic topology.

## 1,667 Citations

### Contemporary Mathematics Lectures on the Cohomology of Finite Groups

- Mathematics
- 2006

These are notes based on lectures given at the summer school “Interactions Between Homotopy Theory and Algebra”, which was held at the University of Chicago in the summer of 2004.

### Lectures on the Cohomology of Finite Groups

- Mathematics
- 2006

In this paper we first survey some basic results in the cohomology of finite groups, and then discuss recent work on constructing free actions of finite groups on products of spheres.

### On the Galois cohomology of ideal class groups

- Mathematics
- 2007

Abstract.We use étale cohomology to prove some explicit results on the Galois cohomology of ideal class groups.

### Infinitesimal cohomology and the Chern character to negative cyclic homology

- Mathematics
- 2007

There is a Chern character from K-theory to negative cyclic homology. We show that it preserves the decomposition coming from Adams operations, at least in characteristic zero.

### Unramified cohomology of finite groups of Lie type

- Mathematics
- 2010

. — We prove vanishing results for unramiﬁed stable cohomology of ﬁnite groups of Lie type.

### Quillen's work in algebraic K -theory

- Mathematics
- 2013

We survey the genesis and development of higher algebraic K-theory by Daniel Quillen.

### Cohomology of special 128-groups 1)

- Mathematics
- 1999

Using the Carlson's functions on calculating the cohomology of p-groups, we obtain the cohomology rings of the special 128-groups.

### Linearization of algebraic group actions

- Mathematics
- 2018

This expository text presents some fundamental results on actions of linear algebraic groups on algebraic varieties: linearization of line bundles and local properties of such actions.

## References

SHOWING 1-10 OF 21 REFERENCES

### Introduction to algebraic K-theory

- Mathematics
- 1971

Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ? an abelian group K0? or K1? respectively. Professor Milnor sets…

### On the homology of congruence subgroups and k(3)(z).

- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1975

The homology and cohomology of Gamma(n;p) as modules over SL (n;F(p)) are studied and an upper bound for the order of K(3)(Z) is obtained.

### On Chern classes of representations of finite groups

- Mathematics
- 1965

(cf. [8], say). Atiyah [ l ] posed the problem of relating the Chern classes of i{K with those of X, for any representation X of H. The purpose of this note is to announce the proof of a conjecture…

### Stable real cohomology of arithmetic groups

- Mathematics
- 1974

Given a discrete subgroup Γ of a connected real semisimple Lie group G with finite center there is a natural homomorphism
$$j_\Gamma ^q:I_G^q \to {H^q}\left( {\Gamma ;c} \right)\quad \left( {q =…

### Euler characteristics of groups: Thep-fractional part

- Mathematics
- 1975

If F is a group satisfying suitable finiteness conditions, then one associates to F a rational number g(F), called the Euler characteristic of F, whose failure to be an integer is closely related to…

### Cohomologie des groupes discrets

- Mathematics
- 1971

© Association des collaborateurs de Nicolas Bourbaki, 1970-1971, tous droits réservés. L’accès aux archives du séminaire Bourbaki (http://www.bourbaki. ens.fr/) implique l’accord avec les conditions…