Least dilatation of pure surface braids

"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."

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2019

Author dc:creator

• Loving, Marissa Kawehi

Contributors dc:contributor

• Leininger, Christopher
• Dunfield, Nathan
• Kapovich, Ilya
• Kent, Autumn

• mapping class groups, pure surface braids, least dilatation, pseudo-Anosov

Statement dc:rights

• Copyright 2019 Marissa Kawehi Loving

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/105626