Homology stability for symplectic groups

Details Homology stability for symplectic groups Homology stability for symplectic groups

2001-10-16

arxiv.org/abs/math/0110163v2

Documenta Mathematica, Vol. 7 (2002), 143-166

Mathematics

K-Theory and Homology

21 pages, LaTeX. Contents have been merged with arXiv:math/0111117 in final publication

Scientific paper

In this paper the homology stability for symplectic groups over a ring with finite stable rank is established. First we develop a `nerve theorem' on the homotopy type of a poset in terms of a cover by subposets, where the cover is itself indexed by a poset. We use the nerve theorem to show that a poset of sequences of isotropic vectors is highly connected, as conjectured by Charney in the eighties.

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