On the Homology of GLnand Higher Pre-Bloch Groups

Abstract

AbstractFor every integern> 1 and infinite fieldFwe construct a spectral sequence converging to the homology of GLn(F) relative to the group of monomial matrices GMn(F). Some entries inE2-terms of these spectral sequences may be interpreted as a natural generalization of the Bloch group to higher dimensions. These groups may be characterized as homology of GLnrelatively to GLn-1and GMn. We apply the machinery developed to the investigation of stabilization maps in homology of General Linear Groups.