Homology stability for linear groups

Wilberd van der Kallen

doi:10.1007/BF01390018

Homology stability for linear groups

Wilberd van der Kallen^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

Let R 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 over R. Applying W.G. Dwyer's arguments (cf. [9]) we also get stability for homology with twisted coefficients. For example, H₂(GL_n(R), Rⁿ) takes on a stable value when n becomes large.

Original language	English
Pages (from-to)	269-295
Number of pages	27
Journal	Inventiones Mathematicae
Volume	60
Issue number	3
DOIs	https://doi.org/10.1007/BF01390018
Publication status	Published - Oct 1980

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title = "Homology stability for linear groups",

abstract = "Let R 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 over R. Applying W.G. Dwyer's arguments (cf. [9]) we also get stability for homology with twisted coefficients. For example, H2(GLn(R), Rn) takes on a stable value when n becomes large.",

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AB - Let R 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 over R. Applying W.G. Dwyer's arguments (cf. [9]) we also get stability for homology with twisted coefficients. For example, H2(GLn(R), Rn) takes on a stable value when n becomes large.

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U2 - 10.1007/BF01390018

DO - 10.1007/BF01390018

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EP - 295

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

IS - 3

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Homology stability for linear groups

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