## Algebraic & Geometric Topology

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

#### 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.

#### Article information

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

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

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

#### 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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