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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, y4} for the Baumslag--Solitar group < x, y | xy2x-1=y3 > is stably free non-free of rank one.

Keywords

2-dimensional complex, homotopy-type, stably free modules
Mathematical Subject Classification

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