University of Illinois Urbana-Champaign

Orderability of homology spheres obtained by Dehn filling

Gao, Xinghua

Content Files
GAO-DISSERTATION-2019.pdf

Permalink

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

Description

Title
Orderability of homology spheres obtained by Dehn filling
Author(s)
Gao, Xinghua
Issue Date
2019-07-03
Director of Research (if dissertation) or Advisor (if thesis)
Dunfield, Nathan M.
Doctoral Committee Chair(s)
Leininger, Christopher J.
Committee Member(s)
  • Allen, Patrick B.
  • Bradlow, Steven B.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2019-11-26T20:33:46Z
Keyword(s)
  • left-orderable group
  • $\widetilde{PSL_2\mathbb{R}}$ representation
Abstract
In my thesis, I study left-orderability of $\mathbb{Q}$-homology spheres. I use $\widetilde{PSL_2\mathbb{R}}$ 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 $\widetilde{PSL_2\mathbb{R}}$ representations. However, this tool is still useful in most cases. With $\widetilde{PSL_2\mathbb{R}}$ 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.
Graduation Semester
2019-08
Type of Resource
text
Permalink
http://hdl.handle.net/2142/105627
Copyright and License Information
Copyright 2019 Xinghua Gao

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