Least dilatation of pure surface braids

We study the minimal dilatation of pseudo-Anosov pure surface braids and provide upper and lower bounds as a function of genus and the number of punctures. For a fixed number of punctures, these bounds tend to infinity as the genus does. We also bound the dilatation of pseudo-Anosov pure surface braids away from zero and give a constant upper bound in the case of a sufficient number of punctures.

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Keywords

mapping class group, pseudo Anosov, dilatation, stretch factor, pure surface braids

Mathematical Subject Classification 2010

Primary: 37E30

Secondary: 20F36, 20F65, 30F60, 37B40, 37D20, 57M07, 57M99

References

Publication

Received: 17 February 2018

Revised: 31 July 2018

Accepted: 13 August 2018

Published: 12 March 2019

Authors

Marissa Loving
Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL United States
https://sites.google.com/view/lovingmath/home
Marissa Loving


Hugo Parlier
Mathematics Research Unit University of Luxembourg Campus Belval Esch-sur-Alzette Luxembourg

Volume 19, issue 2 (2019)

Marissa Loving

Appendix: Marissa Loving and Hugo Parlier

Abstract