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

Access to Document

10.1007/BF01390018

Cite this

@article{eece812f8e6948218d572a7121484e02,

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.",

author = "{van der Kallen}, Wilberd",

year = "1980",

month = oct,

doi = "10.1007/BF01390018",

language = "English",

volume = "60",

pages = "269--295",

journal = "Inventiones Mathematicae",

issn = "0020-9910",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Homology stability for linear groups

AU - van der Kallen, Wilberd

PY - 1980/10

Y1 - 1980/10

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=0000499231&partnerID=8YFLogxK

U2 - 10.1007/BF01390018

DO - 10.1007/BF01390018

M3 - Article

AN - SCOPUS:0000499231

SN - 0020-9910

VL - 60

SP - 269

EP - 295

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

IS - 3

ER -

Homology stability for linear groups

Abstract

Access to Document

Other files and links

Fingerprint

Cite this