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Aspherical Relative Presentations all Over Again

Published online by Cambridge University Press:  15 April 2019

By
William A. Bogley ,
Martin Edjvet  and
Gerald Williams
Edited by
C. M. Campbell ,
C. W. Parker ,
M. R. Quick ,
E. F. Robertson  and
C. M. Roney-Dougal
C. M. Campbell
Affiliation:
University of St Andrews, Scotland
C. W. Parker
Affiliation:
University of Birmingham
M. R. Quick
Affiliation:
University of St Andrews, Scotland
E. F. Robertson
Affiliation:
University of St Andrews, Scotland
C. M. Roney-Dougal
Affiliation:
University of St Andrews, Scotland
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Summary

The concept of asphericity for relative group presentations was introduced twenty-five years ago. Since then, the subject has advanced and detailed asphericity classifications have been obtained for various families of one-relator relative presentations. Through this work the definition of asphericity has evolved and new applications have emerged. In this article we bring together key results on relative asphericity, update them, and exhibit them under a single set of definitions and terminology. We describe consequences of asphericity and present techniques for proving asphericity and for proving non-asphericity. We give a detailed survey of results concerning one-relator relative presentations where the relator has free product length four.

Type
Chapter
Information
Groups St Andrews 2017 in Birmingham , pp. 169 - 199
Publisher: Cambridge University Press
Print publication year: 2019

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