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Title:Least dilatation of pure surface braids
Author(s):Loving, Marissa Kawehi
Director of Research:Leininger, Christopher
Doctoral Committee Chair(s):Dunfield, Nathan
Doctoral Committee Member(s):Kapovich, Ilya; Kent, Autumn
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):mapping class groups, pure surface braids, least dilatation, pseudo-Anosov
Abstract:This thesis finds its roots in the Nielsen-Thurston classification of the mapping class group, a result that is fundamental to the field of low dimensional topology. In particular, Thurston's work gives us a powerful normal form for mapping classes: up to taking powers and restricting to subsurfaces, every mapping class can be decomposed into pieces which are either the identity or pseudo-Anosov. Associated to each of these pseudo-Anosov mapping classes is a unique algebraic number called its dilatation or ``stretch-factor". In this thesis, we build on work of Penner who introduced the study of the minimal dilatation of pseudo-Anosovs in subgroups of the mapping class group. We prove upper and lower bounds on the minimal dilatation of pseudo-Anosovs in the $n$-stranded pure surface braid group extending results of Aougab--Taylor and Dowdall for the 1-stranded pure surface braid group.
Issue Date:2019-07-02
Type:Text
URI:http://hdl.handle.net/2142/105626
Rights Information:Copyright 2019 Marissa Kawehi Loving
Date Available in IDEALS:2019-11-26
Date Deposited:2019-08


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