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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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