The sphericity of the complex of non-degenerate subspaces
Combinatorics
2015-03-27 v3 Group Theory
Abstract
We prove that the complex of proper non-trivial non-degenerate subspaces of a finite-dimensional vector space endowed with a non-degenerate sesquilinear form is homotopy equivalent to a wedge of spheres. Additionally, we show that the same is true for a slight generalization, the so-called generalized Phan geometries of type A_n. These generalized Phan geometries occur as relative links of certain filtrations. Their sphericity implies finiteness properties of suitable arithmetic groups and allows for a revision of Phan's group-theoretical local recognition of suitable finite groups of Lie type with simply laced diagram.
Keywords
Cite
@article{arxiv.0711.3468,
title = {The sphericity of the complex of non-degenerate subspaces},
author = {Alice Devillers and Ralf Köhl and Bernhard Muhlherr},
journal= {arXiv preprint arXiv:0711.3468},
year = {2015}
}