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Aspherical Relative Presentations All Over Again

Williams, Gerald and Bogley, William A and Edjvet, Martin (2019) 'Aspherical Relative Presentations All Over Again.' In: Campbell, CM and Quick, MR and Parker, CW and Robertson, EF and Roney-Dougal, CM, (eds.) Groups St Andrews 2017 in Birmingham. London Mathematical Society Lecture Note Series . Cambridge University Press. ISBN 9781108728744, 110872874X (In Press)

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Abstract

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.

Item Type: Book Section
Uncontrolled Keywords: Mathematics
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 18 Jan 2019 09:49
Last Modified: 18 Jan 2019 09:49
URI: http://repository.essex.ac.uk/id/eprint/23845

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