Non-orientable surface-plus-one-relation groups

Yago Antolín; Warren Dicks; Peter A. Linnell

doi:10.1016/j.jalgebra.2009.03.001

Non-orientable surface-plus-one-relation groups

Yago Antolín, Warren Dicks, Peter A. Linnell

Department of Mathematics

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

4 Citations (Scopus)

Abstract

Recently Dicks-Linnell determined the L2-Betti numbers of the orientable surface-plus-one-relation groups, and their arguments involved some results that were obtained topologically by Hempel and Howie. Using algebraic arguments, we now extend all these results of Hempel and Howie to a larger class of two-relator groups, and we then apply the extended results to determine the L2-Betti numbers of the non-orientable surface-plus-one-relation groups. © 2009 Elsevier Inc.

Original language	English
Pages (from-to)	4-33
Journal	Journal of Algebra
Volume	326
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2009.03.001
Publication status	Published - 15 Jan 2011

Keywords

L2-Betti number
Surface-plus-one-relation group

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10.1016/j.jalgebra.2009.03.001

Cite this

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title = "Non-orientable surface-plus-one-relation groups",

abstract = "Recently Dicks-Linnell determined the L2-Betti numbers of the orientable surface-plus-one-relation groups, and their arguments involved some results that were obtained topologically by Hempel and Howie. Using algebraic arguments, we now extend all these results of Hempel and Howie to a larger class of two-relator groups, and we then apply the extended results to determine the L2-Betti numbers of the non-orientable surface-plus-one-relation groups. {\textcopyright} 2009 Elsevier Inc.",

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AU - Dicks, Warren

AU - Linnell, Peter A.

PY - 2011/1/15

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N2 - Recently Dicks-Linnell determined the L2-Betti numbers of the orientable surface-plus-one-relation groups, and their arguments involved some results that were obtained topologically by Hempel and Howie. Using algebraic arguments, we now extend all these results of Hempel and Howie to a larger class of two-relator groups, and we then apply the extended results to determine the L2-Betti numbers of the non-orientable surface-plus-one-relation groups. © 2009 Elsevier Inc.

AB - Recently Dicks-Linnell determined the L2-Betti numbers of the orientable surface-plus-one-relation groups, and their arguments involved some results that were obtained topologically by Hempel and Howie. Using algebraic arguments, we now extend all these results of Hempel and Howie to a larger class of two-relator groups, and we then apply the extended results to determine the L2-Betti numbers of the non-orientable surface-plus-one-relation groups. © 2009 Elsevier Inc.

KW - L2-Betti number

KW - Surface-plus-one-relation group

U2 - 10.1016/j.jalgebra.2009.03.001

DO - 10.1016/j.jalgebra.2009.03.001

M3 - Article

SN - 0021-8693

VL - 326

SP - 4

EP - 33

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -

Non-orientable surface-plus-one-relation groups

Abstract

Keywords

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