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ON THE ASPHERICITY OF LENGTH FIVE RELATIVE GROUP PRESENTATIONS

Published online by Cambridge University Press:  16 January 2001

J. HOWIE  and
V. METAFTSIS
J. HOWIE
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, [email protected]
V. METAFTSIS
Affiliation:
Department of Mathematics, University of the Aegean, Karlovassi, GR-83 200 Samos, [email protected]
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Abstract

We investigate asphericity of the relative group presentation $$\langle G,t\mid atbtctdtet=1\rangle$$ and prove it aspherical provided the subgroup of $G$ generated by $$\{ ab^{-1}, bc^{-1}, cd^{-1}, de^{-1}\}$$ is neither finite cyclic nor a finite triangle group. We also prove a similar result for the closely related relative group presentation $$\langle G,s,t \mid \alpha s\beta s\gamma t= 1=\delta t\varepsilon t\zeta s^{-1}\rangle. 2000 Mathematics Subject Classification: 20F05, 57M05.

Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 82 , Issue 1 , January 2001 , pp. 173 - 194
Copyright
2001 London Mathematical Society

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