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Punctured JSJ Tori and Tautological Extensions of Azumaya Algebras / Yi Wang.
- Format:
- Book
- Thesis/Dissertation
- Author/Creator:
- Wang, Yi, author.
- Language:
- English
- Subjects (All):
- Theoretical mathematics.
- Mathematics.
- Applied mathematics.
- Mathematics--Penn dissertations.
- Penn dissertations--Mathematics.
- Local Subjects:
- Theoretical mathematics.
- Mathematics.
- Applied mathematics.
- Mathematics--Penn dissertations.
- Penn dissertations--Mathematics.
- Physical Description:
- 1 online resource (88 pages)
- Contained In:
- Dissertations Abstracts International 85-12B.
- Place of Publication:
- [Philadelphia, Pennsylvania] : University of Pennsylvania, 2022.
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- Language Note:
- English
- Summary:
- The SL2(ℂ) character variety X(M) has emerged as an important tool in studying the topology of hyperbolic 3-manifolds. Chinburg et al. (2022) constructed arithmetic invariants stemming from a canonical quaternion algebra over the normalization of an irreducible component of X(M) containing a lift of the holonomy representation of M. We provide an explicit topological criterion for extending the canonical quaternion algebra over an ideal point, potentially leading to finer arithmetic invariants than those derived in Chinburg et al. (2022). This topological criterion involves Culler-Shalen theory (Culler and Shalen (1983)) and, in some cases, JSJ decompositions of toroidal Dehn fillings of knot complements in the three-sphere. Inspired by the work of Paoluzzi and Porti (2012) and Tillmann (2012), we provide examples of several cases where these refined invariants exist. Along the way, we show that certain families of once- and twice-punctured tori in hyperbolic knot complements can be associated with ideal points of character varieties.
- Notes:
- Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
- Advisors: Chinburg, Ted; Committee members: Merling, Mona; Stover, Matthew.
- Department: Mathematics.
- Ph.D. University of Pennsylvania 2024.
- Local Notes:
- School code: 0175
- ISBN:
- 9798382830025
- Access Restriction:
- Restricted for use by site license.
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