Geodesic
Homology stability for unitary groups
Documenta mathematica, Tome 7 (2002), pp. 143-166.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper the homology stability for unitary groups over a ring with finite unitary 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. Homology stability of symplectic groups and orthogonal groups appear as a special case of our results.
Classification : 19G99, 11E70, 18G30, 19B10
Keywords: poset, acyclicity, unitary groups, homology stability 
@article{DOCMA_2002__7__a13,
     author = {Mirzaii, B. and van der Kallen, W.},
     title = {Homology stability for unitary groups},
     journal = {Documenta mathematica},
     pages = {143--166},
     publisher = {mathdoc},
     volume = {7},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2002__7__a13/}
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Mirzaii, B.; van der Kallen, W. Homology stability for unitary groups. Documenta mathematica, Tome 7 (2002), pp. 143-166. http://geodesic.mathdoc.fr/item/DOCMA_2002__7__a13/