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Search: MSC category 19D55 ( $K$-theory and homology; cyclic homology and cohomology [See also 18G60] )

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1. CJM 2000 (vol 52 pp. 1310)

Yagunov, Serge
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.

Categories:19D55, 20J06, 18G60

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