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Homology stability for linear groups

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LetR be a commutative finite dimensional noetherian ring or, more generally, an associative ring which satisfies one of Bass' stable range conditions. We describe a modified version of H. Maazen's work [18], yielding stability for the homology of linear groups overR. Applying W.G. Dwyer's arguments (cf. [9]) we also get stability for homology with twisted coefficients. For example,H 2(GL n (R), R n) takes on a stable value whenn becomes large.

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  1. Mathematisch Instituut, Rijksuniversiteit Utrecht, Budapestlaan 6, 3508 TA, Utrecht, Niederlande

    Wilberd van der Kallen

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van der Kallen, W. Homology stability for linear groups. Invent Math 60, 269–295 (1980). https://doi.org/10.1007/BF01390018

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  • DOI: https://doi.org/10.1007/BF01390018

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