location:  Publications → journals → CJM
Abstract view

# On the Homology of $\GL_n$ and Higher Pre-Bloch Groups

For every integer $n>1$ and infinite field $F$ we construct a spectral sequence converging to the homology of $\GL_n(F)$ relative to the group of monomial matrices $\GM_n(F)$. Some entries in $E^2$-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 $\GL_n$ relatively to $\GL_{n-1}$ and $\GM_n$. We apply the machinery developed to the investigation of stabilization maps in homology of General Linear Groups.
 MSC Classifications: 19D55 - $K$-theory and homology; cyclic homology and cohomology [See also 18G60] 20J06 - Cohomology of groups 18G60 - Other (co)homology theories [See also 19D55, 46L80, 58J20, 58J22]