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Title:Low dilatation pseudo-anosovs on punctured surfaces and volume
Author(s):Li, Shixuan
Director of Research:Leininger, Christopher
Doctoral Committee Chair(s):Kapovich, Ilya
Doctoral Committee Member(s):Dunfield, Nathan; Bradlow, Steven
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(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.
Issue Date:2020-07-17
Type:Thesis
URI:http://hdl.handle.net/2142/108514
Rights Information:Copyright 2020 by Shixuan Li. All rights reserved.
Date Available in IDEALS:2020-10-07
Date Deposited:2020-08


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