Homology stability for symplectic groups, by Behrooz Mirzaii and Wilberd Van der Kallen

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.

Behrooz Mirzaii <mirzaii@math.uu.nl>
Wilberd Van der Kallen <vdkallen@math.uu.nl>