  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.
