Geodesic
Homology stability for unitary groups
Documenta mathematica, Tome 7 (2002), pp. 143-166
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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.
DOI : 10.4171/dm/121
Classification : 11E70, 19B10, 19G99
Mots-clés : poset, unitary groups, acyclicity, homology stability 
@article{10_4171_dm_121,
     author = {B. Mirzaii and W. van der Kallen},
     title = {Homology stability for unitary groups},
     journal = {Documenta mathematica},
     pages = {143--166},
     year = {2002},
     volume = {7},
     doi = {10.4171/dm/121},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/121/}
}
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B. Mirzaii; W. van der Kallen. Homology stability for unitary groups. Documenta mathematica, Tome 7 (2002), pp. 143-166. doi: 10.4171/dm/121

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