L 2-Betti numbers of one-relator groups

Warren Dicks; Peter A. Linnell

doi:https://doi.org/10.1007/s00208-006-0058-y

L ²-Betti numbers of one-relator groups

Warren Dicks, Peter A. Linnell

Department of Mathematics

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

18 Citations (Scopus)

Abstract

We determine the L 2-Betti numbers of all one-relator groups and all surface-plus-one-relation groups. We also obtain some information about the L 2-cohomology of left-orderable groups, and deduce the non-L 2 result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free. © Springer-Verlag 2007.

Original language	English
Pages (from-to)	855-874
Journal	Mathematische Annalen
Volume	337
DOIs	https://doi.org/10.1007/s00208-006-0058-y
Publication status	Published - 1 Apr 2007

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title = "L 2-Betti numbers of one-relator groups",

abstract = "We determine the L 2-Betti numbers of all one-relator groups and all surface-plus-one-relation groups. We also obtain some information about the L 2-cohomology of left-orderable groups, and deduce the non-L 2 result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free. {\textcopyright} Springer-Verlag 2007.",

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AU - Linnell, Peter A.

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N2 - We determine the L 2-Betti numbers of all one-relator groups and all surface-plus-one-relation groups. We also obtain some information about the L 2-cohomology of left-orderable groups, and deduce the non-L 2 result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free. © Springer-Verlag 2007.

AB - We determine the L 2-Betti numbers of all one-relator groups and all surface-plus-one-relation groups. We also obtain some information about the L 2-cohomology of left-orderable groups, and deduce the non-L 2 result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free. © Springer-Verlag 2007.

U2 - https://doi.org/10.1007/s00208-006-0058-y

DO - https://doi.org/10.1007/s00208-006-0058-y

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VL - 337

SP - 855

EP - 874

JO - Mathematische Annalen

JF - Mathematische Annalen

ER -

L 2-Betti numbers of one-relator groups

Abstract

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L ²-Betti numbers of one-relator groups