Algebraic & Geometric Topology

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

Jens Harlander and Jacqueline A Jensen

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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|xy2x1=y3 is stably free non-free of rank one.

Article information

Source
Algebr. Geom. Topol., Volume 6, Number 5 (2006), 2163-2173.

Dates
Received: 18 May 2006
Accepted: 25 September 2006
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796633

Digital Object Identifier
doi:10.2140/agt.2006.6.2163

Mathematical Reviews number (MathSciNet)
MR2263062

Zentralblatt MATH identifier
1128.57002

Subjects
Primary: 57M20: Two-dimensional complexes
Secondary: 57M05: Fundamental group, presentations, free differential calculus

Keywords
2-dimensional complex homotopy-type stably free modules

Citation

Harlander, Jens; Jensen, Jacqueline A. Exotic relation modules and homotopy types for certain 1–relator groups. Algebr. Geom. Topol. 6 (2006), no. 5, 2163--2173. doi:10.2140/agt.2006.6.2163. https://projecteuclid.org/euclid.agt/1513796633


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References

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