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

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.

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Keywords

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

Mathematical Subject Classification 2000

Primary: 57M20

Secondary: 57M05

References

Forward citations

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)

Jens Harlander and Jacqueline A Jensen

Abstract