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The Quarterly Journal of Mathematics Advance Access published online on June 10, 2008
The Quarterly Journal of Mathematics, doi:10.1093/qmath/han015
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© The author 2008. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

FREIHEITSSÄTZE FOR ONE-RELATOR QUOTIENTS OF SURFACE GROUPS AND OF LIMIT GROUPS

James Howie{dagger} and Muhammad Sarwar Saeed {ddagger}

Department of Mathematics and Maxwell Institute of Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK

{dagger} Corresponding author. E-mail: jim{at}ma.hw.ac.uk

Received 26 October 2007; revised 14 April 2008
  Abstract

Three versions of the Freiheitssatz are proved in the context of one-relator quotients of limit groups, where the latter are equipped with 1-acylindrical splittings over cyclic subgroups. These are natural extensions of previously published corresponding statements for one-relator quotients of orientable surface groups. Two of the proofs are new even in that restricted context.

{ddagger} E-mail: mssaeed{at}ma.hw.ac.uk


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