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

Kazuhiro Hikami, Jeremy Lovejoy

    Research output: Contribution to journalArticlepeer-review

    6 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)249-272
    Number of pages24
    JournalCommunications in Number Theory and Physics
    Volume11
    Issue number2
    DOIs
    Publication statusPublished - 2017

    All Science Journal Classification (ASJC) codes

    • Algebra and Number Theory
    • Mathematical Physics
    • General Physics and Astronomy

    Fingerprint

    Dive into the research topics of 'Hecke-type formulas for families of unified Witten-Reshetikhin-Turaev invariants'. Together they form a unique fingerprint.

    Cite this