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.
Harlander, Jens 1 ; Jensen, Jacqueline A 2
@article{10_2140_agt_2006_6_2163,
author = {Harlander, Jens and Jensen, Jacqueline A},
title = {Exotic relation modules and homotopy types for certain 1{\textendash}relator groups},
journal = {Algebraic and Geometric Topology},
pages = {2163--2173},
year = {2006},
volume = {6},
number = {5},
doi = {10.2140/agt.2006.6.2163},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.2163/}
}
TY - JOUR AU - Harlander, Jens AU - Jensen, Jacqueline A TI - Exotic relation modules and homotopy types for certain 1–relator groups JO - Algebraic and Geometric Topology PY - 2006 SP - 2163 EP - 2173 VL - 6 IS - 5 UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.2163/ DO - 10.2140/agt.2006.6.2163 ID - 10_2140_agt_2006_6_2163 ER -
%0 Journal Article %A Harlander, Jens %A Jensen, Jacqueline A %T Exotic relation modules and homotopy types for certain 1–relator groups %J Algebraic and Geometric Topology %D 2006 %P 2163-2173 %V 6 %N 5 %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.2163/ %R 10.2140/agt.2006.6.2163 %F 10_2140_agt_2006_6_2163
Harlander, Jens; Jensen, Jacqueline A. Exotic relation modules and homotopy types for certain 1–relator groups. Algebraic and Geometric Topology, Tome 6 (2006) no. 5, pp. 2163-2173. doi: 10.2140/agt.2006.6.2163
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