Free products of abelian groups in mapping class groups

The notions of convex cocompactness and geometric finiteness originally come from the study of Kleinian groups. The analogous notion of convex cocompactness for mapping class groups is due to Farb-Mosher. In recent work, Dowdall-Durham-Leininger-Sisto have proposed a definition of “parabolic” geometric finiteness for mapping class groups. In this thesis, we construct a new family of examples of parabolically geometrically finite mapping class subgroups and prove that they are undistorted in Mod(S). We also prove that a subfamily of our examples are also geometrically finite in the sense of Durham-Hagen-Sisto.

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

2022

Author dc:creator

• Loa, Christopher

Contributors dc:contributor

• Leininger, Christopher J
• Dunfield, Nathan
• Bradlow, Steven
• Sadanand, Chandrika

• geometry
• topology

Statement dc:rights

• Copyright 2021 Christopher Loa

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/113005

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/113005