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Surface groups, infinite generating sets, and stable commutator length

Published online by Cambridge University Press:  23 April 2019

Dan Margalit  and
Andrew Putman
Dan Margalit
Affiliation:
Georgia Institute of Technology, School of Mathematics, 686 Cherry St, Atlanta, GA30306, USA (margalit@math.gatech.edu)
Andrew Putman
Affiliation:
Department of Mathematics, University of Notre Dame, 255 Hurley Hall, Notre Dame, IN46556, USA (andyp@nd.edu)
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Abstract

We give a new proof of a theorem of D. Calegari that says that the Cayley graph of a surface group with respect to any generating set lying in finitely many mapping class group orbits has infinite diameter. This applies, for instance, to the generating set consisting of all simple closed curves.

Keywords

Surface groupstable commutator lengthmapping class group
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 5 , October 2020 , pp. 2379 - 2386
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Copyright
Copyright © Royal Society of Edinburgh 2019

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