Volume 19, issue 2 (2019)

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Least dilatation of pure surface braids

Marissa Loving

Appendix: Marissa Loving and Hugo Parlier

Algebraic & Geometric Topology 19 (2019) 941–964

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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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
Received: 17 February 2018
Revised: 31 July 2018
Accepted: 13 August 2018
Published: 12 March 2019
Marissa Loving
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL
United States
Marissa Loving
Hugo Parlier
Mathematics Research Unit
University of Luxembourg
Campus Belval