Related papers: Sectional rank and Cohomology

We investigate bounds on the dimension of cohomology groups for finite groups acting on an irreducible kG-module for G a finite group of bound sectional p-rank and k an algebraically closed field of characteristic p.

Let $G$ be a finitely generated infinite group and let $p > 1$. In this paper we make a connection between the first $L^p$-cohomology space of $G$ and $p$-harmonic functions on $G$. We also describe the elements in the first…

Let G be an infinite discrete group of type FP-infinity and let p>1 be a real number. We prove that the l^p-homology and cohomology groups of G are either 0 or infinite dimensional. We also show that the cardinality of the p-harmonic…

We prove that for any prime $p$ the finite $p$-groups of fixed coclass have only finitely many different mod-$p$ cohomology rings between them. This was conjectured by Carlson; we prove it by first proving a stronger version for groups of…

We generalise to profinite groups some of our previous results on the cohomology of pro-p groups of bounded sectional p-rank.

Let G be a noncocompact irreducible arithmetic group over a global function field K of characteristic p, and let H be a finite-index, residually p-finite subgroup of G. We show that the cohomology of H in the dimension of its associated…

Let G be a finite group of Lie type, defined over a field k of characteristic p > 0. We find explicit bounds for the dimension of the first cohomology group for G with coefficients in a simple kG-module. We proceed by bounding the number of…

Bounded-cohomological dimension of groups is a relative of classical cohomological dimension, defined in terms of bounded cohomology with trivial coefficients instead of ordinary group cohomology. We will discuss constructions that lead to…

We compare the notions of essential dimension and stable cohomological dimension of a finite group G, prove that the latter is bounded by the length of any normal series with cyclic quotients for G, and show that, however, this bound is not…

Let $k$ be an algebraically closed field of characteristic $p > 0$, and let $G$ be a simple simply-connected algebraic group over $k$ that is defined and split over the prime field $\mathbb{F}_p$. In this paper we investigate situations…

Let $p$ be a real number greater than one. In this paper we study the vanishing and nonvanishing of the first $L^p$-cohomology space of some groups that have one end. We also make a connection between the first $L^p$-cohomology space and…

Let $p$ be a fixed prime number and let $R$ denote a uniserial $p$-adic space group of dimension $d_x=(p-1)p^{x-1}$ and with cyclic point group of order $p^x$. In this short note we prove that all the quotients of $R$ of size bigger than or…

We examine second bounded cohomology and mod p homology in finite index subgroups of 1-relator groups and groups with a presentation of deficiency at least one. We use this to determine exactly which 1-relator groups are boundedly…

We prove that for geometrically finite groups cohomological dimension of the direct product of a group with itself equals 2 times the cohomological dimension dimension of the group.

We investigate two open questions in a cohomology theory relative to the family of finite subgroups. The problem of whether the F-cohomological dimension is subadditive is reduced to extensions by groups of prime order. We show that every…

Consider the configuration spaces of manifolds. We give a precise formula for the integral cohomological dimension (the degree of top non-trivial integral cohomology group) of unordered configuration spaces of manifolds with non-trivial…

We give a lower bound for the exponent of certain elements in the integral cohomology of the total spaces of principal BC-bundles for C a finite cyclic group. As applications we give a proof of the theorem of A. Adem and H.-W. Henn that a…

We compute the mod $p$ cohomology algebra of a family of infinite discrete Kac-Moody groups of rank two defined over finite fields of characteristic different from $p$.

We compute the cohomology with group ring coefficients of the complement of a finite collection of affine hyperplanes in a finite dimensional complex vector space. It is nonzero in exactly one degree, namely the degree equal to the rank of…

We compute the graded rank of the cohomology of the hyperplane complement associated with a quaternionic reflection group, and observe that it factors into irreducible factors with positive integer coefficients. For an irreducible group,…