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Title:Knot complements and 3-manifolds
Author(s):Su, Lecheng
Advisor(s):Mineyev, Igor
Department / Program:Mathematics
Discipline:Applied Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:M.S.
Genre:Thesis
Subject(s):3-manifold, knot complement, cube complex, geometric group theory
Abstract:The study of 3-manifold groups has reached big success in the last few decades, with the proof of geometrization theorem by Perelman, and several virtually compact special theorems by Wise, etc. In this paper, we will explore several aspects of 3-manifold groups and see what it shows for the knot complement as a compact 3-manifold. We will also apply some combinatorial methods in three-manifold topology to the study of the presentation of the knot complement.
Issue Date:2021-04-26
Type:Thesis
URI:http://hdl.handle.net/2142/110496
Rights Information:Copyright 2021 Lecheng Su
Date Available in IDEALS:2021-09-17
Date Deposited:2021-05


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