Classifying spaces with virtually cyclic stabilizers for linear groups

Dieter Dries Degrijse; Ralf  Köhl; Nansen  Petrosyan

doi:10.1007/s00031-015-9307-z

Classifying spaces with virtually cyclic stabilizers for linear groups

Dieter Dries Degrijse, Ralf Köhl, Nansen Petrosyan

Department of Mathematical Sciences

2 Citations (Scopus)

Abstract

We show that every discrete subgroup of GL(n, ℝ) admits a finite-dimensional classifying space with virtually cyclic stabilizers. Applying our methods to SL(3, ℤ), we obtain a four-dimensional classifying space with virtually cyclic stabilizers and a decomposition of the algebraic K-theory of its group ring.

Original language	English
Journal	Transformation Groups
Volume	20
Issue number	2
Pages (from-to)	381-394
ISSN	1083-4362
DOIs	https://doi.org/10.1007/s00031-015-9307-z
Publication status	Published - 2015

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10.1007/s00031-015-9307-z

http://arxiv.org/abs/1402.4749

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title = "Classifying spaces with virtually cyclic stabilizers for linear groups",

abstract = "We show that every discrete subgroup of GL(n, ℝ) admits a finite-dimensional classifying space with virtually cyclic stabilizers. Applying our methods to SL(3, ℤ), we obtain a four-dimensional classifying space with virtually cyclic stabilizers and a decomposition of the algebraic K-theory of its group ring.",

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AU - Degrijse, Dieter Dries

AU - Köhl, Ralf

AU - Petrosyan, Nansen

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N2 - We show that every discrete subgroup of GL(n, ℝ) admits a finite-dimensional classifying space with virtually cyclic stabilizers. Applying our methods to SL(3, ℤ), we obtain a four-dimensional classifying space with virtually cyclic stabilizers and a decomposition of the algebraic K-theory of its group ring.

AB - We show that every discrete subgroup of GL(n, ℝ) admits a finite-dimensional classifying space with virtually cyclic stabilizers. Applying our methods to SL(3, ℤ), we obtain a four-dimensional classifying space with virtually cyclic stabilizers and a decomposition of the algebraic K-theory of its group ring.

U2 - 10.1007/s00031-015-9307-z

DO - 10.1007/s00031-015-9307-z

M3 - Journal article

SN - 1083-4362

VL - 20

SP - 381

EP - 394

JO - Transformation Groups

JF - Transformation Groups

IS - 2

ER -

Classifying spaces with virtually cyclic stabilizers for linear groups

Abstract

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