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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 |
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| Type of Resource: | text | |
| Genre: |
Text Doctoral Thesis |
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| Issuance: | monographic | |
| Date Issued: | 2017 | |
| Publisher: | Florida State University | |
| Place of Publication: | Tallahassee, Florida | |
| Physical Form: |
computer online resource |
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| 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 | |
| Host Institution: | FSU |
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
