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Homology stability for symplectic groups

B. Mirzaii·W. van der Kallen
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Abstract

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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B. Mirzaii, W. van der Kallen. 2012-01-05. Homology stability for symplectic groups. https://arxiv.org/abs/math/0110163

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