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

Kazuhiro Hikami, Jeremy Lovejoy

研究成果: Contribution to journalArticle査読

4 被引用数 (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.

本文言語英語
ページ(範囲)249-272
ページ数24
ジャーナルCommunications in Number Theory and Physics
11
2
DOI
出版ステータス出版済み - 2017

All Science Journal Classification (ASJC) codes

  • 代数と数論
  • 数理物理学
  • 物理学および天文学(全般)

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