A Lie algebra L is said to be of cohomological dimension 1, if H(L, M) = 0 for any L-module M . Due to the standard interpretation of the second cohomology group, this is equivalent to the condition that each exact sequence 0 → M → G → L → 0 splits. Of course, the cohomological dimension may be defined via standard devices of homological algebra – e.g. as the minimal length of the projective re...

For each d ∈ N we construct a 3-generated group Hd, which is a subdirect product of free groups, such that the cohomological dimension of Hd is d. Given a group F and a normal subgroup N C F we prove that any right angled Artin group containing the special HNN-extension of F with respect to N must also contain F/N . We apply this to construct, for every d ∈ N, a 4-generated group Gd, embeddable...

The aim of this paper is to split the assembly map in Kand L-theory for a class of groups of finite cohomological dimension, containing the word hyperbolic groups

We show that, if g ≥ 2, the virtual cohomological dimension of the mapping class group of a 3-dimensional handlebody of genus g is equal to 4g − 5 and the Euler number of it is equal to 0.

A discrete group G has periodic cohomology over R if there is an element α ∈ Ext RG (R,R) of positive degree and an integer n ≥ 0 such that the cup product map by α induces an isomorphism of Ext RG (R,−) and Ext i+|α| RG (R,−) for i ≥ n. Adem and Smith [1] showed if R = Z, then this condition is equivalent to the existence of a finite dimensional free-G-CW-complex homotopy equivalent to a spher...

We show that for certain discrete p-perfect groups G, in particular for all pperfect groups of finite cohomological dimension, the loop space on the p-completed classifying space ΩBGp is a retract of the loop spaces on a certain finite complex. For finite vcd groups we provide a bound on the the dimension of such a complex.

In this paper, considering the difference between the finiteness dimension and cohomological dimension for a finitely generated module, we investigate the asymptotic behavior of grades of components of graded local cohomology modules with respect to irrelevant ideal; as long as we study some artinian and tameness property of such modules.