Factorable Groups and their Homology

Abstract

In this thesis we introduce the class of factorable groups. These are normed groups together with a norm preserving decemposition (or factorization) of each group element into two factors. <br /> Already the norm alone gives a filtration of the bar resolution and of the bar complex, which we call the norm filtration and we study the spectral sequence associated to the norm filtration. <br /> The main result of the thesis is that for a factorable group the homology of the columns of the E^0-term is concentrated in the top degree. Consequently, the spectral sequence associated to the norm filtration collapses after the E^2-term and the homology of the group G can be computed as the homology of the E^1-term.<br /> Moreover, using the structure of a factorable group G we can find a free resolution of Z over ZG which has fewer generators than the bar resolution, making computations easier.