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On the Homology of $\GL_n$ and Higher Pre-Bloch Groups |
Canad. J. Math. 52(2000), 1310-1338
Published:2000-12-01
Printed: Dec 2000
Printed: Dec 2000
- Serge Yagunov
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 - $K$-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] |