University of Illinois Urbana-Champaign

Low dilatation pseudo-anosovs on punctured surfaces and volume

Li, Shixuan

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

Description

Title
Low dilatation pseudo-anosovs on punctured surfaces and volume
Author(s)
Li, Shixuan
Issue Date
2020-07-17
Director of Research (if dissertation) or Advisor (if thesis)
Leininger, Christopher
Doctoral Committee Chair(s)
Kapovich, Ilya
Committee Member(s)
  • Dunfield, Nathan
  • Bradlow, Steven
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • pseudo-Anosovs
  • volume
  • punctured surfaces
  • mapping torus
Abstract
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.
Graduation Semester
2020-08
Type of Resource
Thesis
Permalink
http://hdl.handle.net/2142/108514
Copyright and License Information
Copyright 2020 by Shixuan Li. All rights reserved.

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