國立虎尾科技大學 |

q-Holonomic Systems and Quantum Invariants.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	q-Holonomic Systems and Quantum Invariants./
作者:	Brown, Jennifer M.
面頁冊數:	1 online resource (60 pages)
附註:	Source: Dissertations Abstracts International, Volume: 84-03, Section: B.
Contained By:	Dissertations Abstracts International84-03B.
標題:	Mathematics. -
電子資源:	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.
LDR:02357ntm a22003737 4500 001 1148134
005 20240916070008.5
006 m o d
007 cr bn ---uuuuu
008 250605s2022 xx obm 000 0 eng d
020 $a 9798841790297
035 $a (MiAaPQ)AAI29069324
035 $a AAI29069324
040 $a MiAaPQ $b eng $c MiAaPQ $d NTU
100 1 $a Brown, Jennifer M. $3 1474041
245 1 0 $a q-Holonomic Systems and Quantum Invariants.
264 0 $c 2022
300 $a 1 online resource (60 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 84-03, Section: B.
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.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
653 $a Holonomic
653 $a Knot
653 $a Quantum
653 $a Recursion
653 $a Topology
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of California, Davis. $b Mathematics. $3 1180526
773 0 $t Dissertations Abstracts International $g 84-03B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29069324 $z click for full text (PQDT)