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Character Varieties of Knots and Links with Symmetries

Title: Character Varieties of Knots and Links with Symmetries.
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Name(s): Sparaco, Leona H., author
Petersen, Kathleen L., professor directing dissertation
Harper, Kristine, university representative
Ballas, Sam, committee member
Bowers, Philip L., 1956-, committee member
Hironaka, Eriko, 1962-, committee member
Florida State University, degree granting institution
College of Arts and Sciences, degree granting college
Department of Mathematics, degree granting department
Type of Resource: text
Genre: Text
Doctoral Thesis
Issuance: monographic
Date Issued: 2017
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource (68 pages)
Language(s): English
Abstract/Description: : Let M be a hyperbolic manifold. The SL2(C) character variety of M is essentially the set of all representations ρ : π1(M) → SL2(C) up to trace equivalence. This algebraic set is connected to many geometric properties of the manifold M. We examine the effect of symmetries of M on its character variety. We compute the SL2(C) and PSL2(C) character varieties for an infinite family of two-bridge hyperbolic knots with symmetry. We explore the effect the symmetry has on the character variety and exploit this symmetry to factor the character variety. We then find the geometric genus of both components of the character variety. We compute the SL2(C) character variety for the Borromean ring complement in S^3. Further, we explore how the symmetries effect this character variety. Finally, we prove some general results about the structure of character varieties of links with symmetries.
Identifier: FSU_SUMMER2017_Sparaco_fsu_0071E_13851 (IID)
Submitted Note: A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Summer Semester 2017.
Date of Defense: July 6, 2017.
Bibliography Note: Includes bibliographical references.
Advisory Committee: Kathleen Petersen, Professor Directing Dissertation; Kristine Harper, University Representative; Sam Ballas, Committee Member; Philip Bowers, Committee Member; Eriko Hironaka, Committee Member.
Subject(s): Mathematics
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_SUMMER2017_Sparaco_fsu_0071E_13851
Owner Institution: FSU

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Sparaco, L. H. (2017). Character Varieties of Knots and Links with Symmetries. Retrieved from http://purl.flvc.org/fsu/fd/FSU_SUMMER2017_Sparaco_fsu_0071E_13851