CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

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

  Published:2000-12-01
 Printed: Dec 2000
  • Serge Yagunov
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

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, 20J06, 18G60 show english descriptions $K$-theory and homology; cyclic homology and cohomology [See also 18G60]
Cohomology of groups
Other (co)homology theories [See also 19D55, 46L80, 58J20, 58J22]
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]
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/