Exotic relation modules and homotopy types for certain 1–relator groups

Harlander, Jens; Jensen, Jacqueline A

doi:10.2140/agt.2006.6.2163

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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Exotic relation modules and homotopy types for certain 1–relator groups

Jens Harlander and Jacqueline A Jensen

Algebraic & Geometric Topology 6 (2006) 2163–2173

DOI: 10.2140/agt.2006.6.2163

arXiv: 0906.5491

Abstract

Using stably free non-free relation modules we construct an infinite collection of 2–dimensional homotopy types, each of Euler-characteristic one and with trefoil fundamental group. This provides an affirmative answer to a question asked by Berridge and Dunwoody [J. London Math. Soc. 19 (1979) 433–436]. We also give new examples of exotic relation modules. We show that the relation module associated with the generating set ${x, y^{4}}$ for the Baumslag–Solitar group $〈 x, y | x y^{2} x^{- 1} = y^{3} 〉$ is stably free non-free of rank one.

Keywords

2-dimensional complex, homotopy-type, stably free modules

Mathematical Subject Classification 2000

Primary: 57M20

Secondary: 57M05

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Publication

Received: 18 May 2006

Accepted: 25 September 2006

Published: 19 November 2006

Authors

Jens Harlander
Department of Mathematics Western Kentucky University Bowling Green, KY 42101 USA

Jacqueline A Jensen
Department of Mathematics and Statistics Sam Houston State University Huntsville, TX 77341 USA

Volume 6, issue 5 (2006)