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Title:Orderability of homology spheres obtained by Dehn filling
Author(s):Gao, Xinghua
Director of Research:Dunfield, Nathan M.
Doctoral Committee Chair(s):Leininger, Christopher J.
Doctoral Committee Member(s):Allen, Patrick B.; Bradlow, Steven B.
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(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.
Issue Date:2019-07-03
Rights Information:Copyright 2019 Xinghua Gao
Date Available in IDEALS:2019-11-26
Date Deposited:2019-08

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