자료유형  

 학위논문

Control Number  

0017160460

International Standard Book Number  

9798382830025

Dewey Decimal Classification Number  

510

Main Entry-Personal Name  

Wang, Yi.

Publication, Distribution, etc. (Imprint  

[S.l.] : University of Pennsylvania., 2024

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2024

Physical Description  

88 p.

General Note  

Source: Dissertations Abstracts International, Volume: 85-12, Section: B.

General Note  

Advisor: Chinburg, Ted.

Dissertation Note  

Thesis (Ph.D.)--University of Pennsylvania, 2024.

Summary, Etc.  

요약The 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.

Subject Added Entry-Topical Term  

Theoretical mathematics.

Subject Added Entry-Topical Term  

Mathematics.

Subject Added Entry-Topical Term  

Applied mathematics.

Index Term-Uncontrolled  

Arithmetic invariants

Index Term-Uncontrolled  

Hyperbolic 3-manifolds

Index Term-Uncontrolled  

Culler-Shalen theory

Index Term-Uncontrolled  

Hyperbolic knot

Index Term-Uncontrolled  

Azumaya algebras

Added Entry-Corporate Name  

University of Pennsylvania Mathematics

Host Item Entry  

Dissertations Abstracts International. 85-12B.

Electronic Location and Access  

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Control Number  

joongbu:657362