On the Homology of GLn and Higher Pre-Bloch Groups

Yagunov, Serge

Canadian journal of mathematics, Tome 52 (2000) no. 6, pp. 1310-1338

Résumé

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.

Détail

DOI : 10.4153/CJM-2000-054-9

Mots-clés : 19D55, 20J06, 18G60

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