Low dilatation pseudo-anosovs on punctured surfaces and volume

For a pseudo-Anosov homeomorphism f on a closed surface of genus g greater of equals to 2, for which the entropy is on the order 1/g (the lowest possible order), Farb-Leininger-Margalit showed that the volume of the mapping torus is bounded, independent of g. We show that the analogous result fails for a surface of fixed genus g with n punctures, by constructing pseudo-Anosov homeomorphism with entropy of the minimal order (log n)/n, and volume tending to infinity.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2020

Author dc:creator

• Li, Shixuan

Contributors dc:contributor

• Leininger, Christopher
• Kapovich, Ilya
• Dunfield, Nathan
• Bradlow, Steven

• pseudo-Anosovs
• volume
• punctured surfaces
• mapping torus

Statement dc:rights

• Copyright 2020 by Shixuan Li. All rights reserved.

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/108514

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/108514