Orderability of homology spheres obtained by Dehn filling

In my thesis, I study left-orderability of $\mathbb{Q}$-homology spheres. I use \widetilde{PSL₂\mathbb{R}} representations as a tool. First, I showed this tool has its limitations by constricting a series of $\mathbb{Z}$-homology spheres with potentially left-orderable fundamental groups but no non trivial \widetilde{PSL₂\mathbb{R}} representations. However, this tool is still useful in most cases. With \widetilde{PSL₂\mathbb{R}} representations, I construct the holonomy extension locus of a $\mathbb{Q}$-homology solid torus which is an analog of its translation extension locus. Using extension loci, I study $\mathbb{Q}$-homology 3-spheres coming from Dehn fillings of $\mathbb{Q}$-homology solid tori and construct intervals of orderable Dehn fillings.

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

• Gao, Xinghua

Contributors dc:contributor

• Dunfield, Nathan M.
• Leininger, Christopher J.
• Allen, Patrick B.
• Bradlow, Steven B.

• left-orderable group
• $\widetilde{PSL_2\mathbb{R}}$ representation

Statement dc:rights

• Copyright 2019 Xinghua Gao

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/105627

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/105627