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On the Homology of GLn and Higher Pre-Bloch Groups

Published online by Cambridge University Press:  20 November 2018

Serge Yagunov*
Affiliation:
Max Planck Institute für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany email: yagunov@mpim-bonn.mpg.de Steklov Mathematical Institute (St. Petersburg), Fontanka 27, 191011 St. Petersburg, Russia email: yagunov@pdmi.ras.ru
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Abstract

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For every integer $n\,>\,1$ and infinite field $F$ we construct a spectral sequence converging to the homology of $\text{G}{{\text{L}}_{n}}\left( F \right)$ relative to the group of monomial matrices $\text{G}{{\text{M}}_{n}}\left( F \right)$. 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 $\text{G}{{\text{L}}_{n}}$ relatively to $\text{G}{{\text{L}}_{n-1}}$ and $\text{G}{{\text{M}}_{n}}$. We apply the machinery developed to the investigation of stabilization maps in homology of General Linear Groups.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2000

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