Homological stability for classical groups

2009/05/01 by Jan Essert, Essert, Jan · 1 citation
Mathematics · #20J05 (Primary) 20E42 (Secondary) #FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT) #math.GR #math.KT #msc:20E42 #msc:20J05

paper · pdf · doi:10.48550/arxiv.0905.0071

30 pages; shortened homology part, polishing

arxiv created 2012/09/04 · arxiv updated 2012/09/05

Abstract

Associated to every group with a weak spherical Tits system of rank n+1 with an appropriate rank n subgroup, we construct a relative spectral sequence involving group homology of Levi subgroups of both groups. Using the fact that such Levi subgroups frequently split as semidirect products of smaller groups, we prove homological stability results for unitary groups over division rings with infinite centre as well as for special linear and special orthogonal groups over infinite fields.

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• Buildings, Group Homology and Lattices

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