Hecke-type formulas for families of unified Witten-Reshetikhin-Turaev invariants

Kazuhiro Hikami, Jeremy Lovejoy

研究成果: ジャーナルへの寄稿記事

1 引用 (Scopus)

抄録

Every closed orientable 3-manifold can be constructed by surgery on a link in S3. In the case of surgery along a torus knot, one obtains a Seifert fibered manifold. In this paper we consider three families of such manifolds and study their unified Witten- Reshetikhin-Turaev (WRT) invariants. Thanks to recent computation of the coefficients in the cyclotomic expansion of the colored Jones polynomial for (2, 2t + 1)-torus knots, these WRT invariants can be neatly expressed as q-hypergeometric series which converge inside the unit disk. Using the Rosso-Jones formula and some rather non-standard techniques for Bailey pairs, we find Hecke-type formulas for these invariants. We also comment on their mock and quantum modularity.

元の言語英語
ページ(範囲)249-272
ページ数24
ジャーナルCommunications in Number Theory and Physics
11
発行部数2
DOI
出版物ステータス出版済み - 1 1 2017

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Torus knot
surgery
Surgery
Invariant
Colored Jones Polynomial
modularity
Hypergeometric Series
Cyclotomic
Modularity
Unit Disk
polynomials
Converge
Closed
expansion
Coefficient
coefficients
Family

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Mathematical Physics
  • Physics and Astronomy(all)

これを引用

Hecke-type formulas for families of unified Witten-Reshetikhin-Turaev invariants. / Hikami, Kazuhiro; Lovejoy, Jeremy.

:: Communications in Number Theory and Physics, 巻 11, 番号 2, 01.01.2017, p. 249-272.

研究成果: ジャーナルへの寄稿記事

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