Fox derivatives, group cohomology, and Kazhdan's property (T)..

Abstract

In this talk I will focus on cohomology of finitely presented groups. I plan to investigate two conditions concerning it: vanishing and reducibility. They are generalizations of Kazhdan's property (T). The key tool to prove vanishing and reducibility of group cohomology I shall use is the Fox calculus. A new result about reducibility of cohomology of special linear group of degree three will be announced.