The sphericity of the complex of non-degenerate subspaces
نویسندگان
چکیده
We prove that the complex of proper non-trivial non-degenerate subspaces of a finitedimensional 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 slightly wider class of simplicial complexes, the so-called generalized Phan geometries of type An. These generalized Phan geometries occur as relative links of the filtration studied in [14], whose sphericity implies topological finiteness properties of suitable arithmetic groups and allows for a revision of Phan’s group-theoretical local recognition [21], [22] of suitable finite groups of Lie type with simply laced diagrams.
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