The spericity of the complex of non-degenerate subspaces
- Autores: Alice Devillers, Ralf Gramlich, Bernhard Mühlherr
- Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 79, Nº 3, 2009, págs. 684-700
- Idioma: inglés
- DOI: 10.1112/jlms/jdn088
- Enlaces
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Resumen
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 M¨uhlherr (Forum Math. 19 (2007) 955�970), whose sphericity implies topological finiteness properties of suitable arithmetic groups and allows for a revision of Phan�s group-theoretical local recognition (K.-W.
Phan, J. Austral. Math. Soc. Ser. A (part I) 23 (1977) 67�77; (part II), 129�146) of suitable finite groups of Lie type with simply laced diagrams.
