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q-Holonomic Systems and Quantum Invariants.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	q-Holonomic Systems and Quantum Invariants./
Author:	Brown, Jennifer M.
Description:	1 online resource (60 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 84-03, Section: B.
Contained By:	Dissertations Abstracts International84-03B.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9798841790297

q-Holonomic Systems and Quantum Invariants.
Brown, Jennifer M.

q-Holonomic Systems and Quantum Invariants. - 1 online resource (60 pages)

Source: Dissertations Abstracts International, Volume: 84-03, Section: B.

Thesis (Ph.D.)--University of California, Davis, 2022.

Includes bibliographical references

The topics of this dissertation fall under the purview of quantum topology, which seeks to build connections between the insights and constructions of quantum physics and classical topology. A pivotal theme will be the appearance of topologically interesting q-holonomic systems in quantum invariants. These manifest in the quasiperiodic behavior of Witten-Reshetikhin-Turaev(WRT) invariants, and as certain modules associated to lagrangians in quantized character varieties. This work was motivated by the AJ conjecture (Garoufalidis, 2004; Gukov, 2005), which predicts that these two manifestations are the two sides of a single coin. The main result of this dissertation is that the ADO invariant is q-holonomic, meaning it exhibits strong recursive behavior. Some subtlety is involved in the definition of q-holonomicity in this setting, as the ADO invariant exhibits a topologically uninteresting quasi-periodicity because of the appearance of roots of unity. This invariant is closely related to the colored Jones polynomial of the AJ conjecture, and acts as its analytic continuation.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798841790297Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

HolonomicIndex Terms--Genre/Form:

554714
Electronic books.

q-Holonomic Systems and Quantum Invariants.
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500 $a Advisor: Mulase, Motohico.
502 $a Thesis (Ph.D.)--University of California, Davis, 2022.
504 $a Includes bibliographical references
520 $a The topics of this dissertation fall under the purview of quantum topology, which seeks to build connections between the insights and constructions of quantum physics and classical topology. A pivotal theme will be the appearance of topologically interesting q-holonomic systems in quantum invariants. These manifest in the quasiperiodic behavior of Witten-Reshetikhin-Turaev(WRT) invariants, and as certain modules associated to lagrangians in quantized character varieties. This work was motivated by the AJ conjecture (Garoufalidis, 2004; Gukov, 2005), which predicts that these two manifestations are the two sides of a single coin. The main result of this dissertation is that the ADO invariant is q-holonomic, meaning it exhibits strong recursive behavior. Some subtlety is involved in the definition of q-holonomicity in this setting, as the ADO invariant exhibits a topologically uninteresting quasi-periodicity because of the appearance of roots of unity. This invariant is closely related to the colored Jones polynomial of the AJ conjecture, and acts as its analytic continuation.
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538 $a Mode of access: World Wide Web
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653 $a Recursion
653 $a Topology
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