TITLE

The sphericity of the complex of non-degenerate subspaces

AUTHOR(S)
Alice Devillers; Ralf Gramlich; Bernhard Mühlherr
PUB. DATE
June 2009
SOURCE
Journal of the London Mathematical Society;Jun2009, Vol. 79 Issue 3, p684
SOURCE TYPE
DOC. TYPE
Article
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 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 Devillers and MÃ¼hlherr (Forum Math. 19 (2007) 955â€“970), whose sphericity implies topological finiteness properties of suitable arithmetic groups and allows for a revision of Phans group-theoretical local recognition (K.-W. Phan, J. Austral. Math. Soc. Ser. A (part I) 23 (1977) 67â€“77; (part II), 129â€“146) of suitable finite groups of Lie type with simply laced diagrams.
ACCESSION #
39988782

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