Least dilatation of pure surface braids

Loving, Marissa Kawehi

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https://hdl.handle.net/2142/105626 Copy

Description

Title

Least dilatation of pure surface braids

Author(s)

Loving, Marissa Kawehi

Issue Date

2019-07-02

Director of Research (if dissertation) or Advisor (if thesis)

Leininger, Christopher

Doctoral Committee Chair(s)

Dunfield, Nathan

Committee Member(s)

• Kapovich, Ilya
• Kent, Autumn

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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."

Graduation Semester

2019-08

Type of Resource

text

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http://hdl.handle.net/2142/105626

Copyright and License Information

Copyright 2019 Marissa Kawehi Loving

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