Director of Research (if dissertation) or Advisor (if thesis)
Mineyev, Igor
Department of Study
Mathematics
Discipline
Applied Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Date of Ingest
2021-09-17T01:11:01Z
Keyword(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.
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