On the quantum invariants for the spherical Seifert manifolds

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Abstract

We study the Witten-Reshetikhin-Turaev SU(2) invariant for the Seifert manifolds S 3/Gamma where Γ is a finite subgroup of SU(2). We show that the WRT invariants can be written in terms of the Eichler integral of modular forms with half-integral weight, and we give an exact asymptotic expansion of the invariants by use of the nearly modular property of the Eichler integral. We further discuss that those modular forms have a direct connection with the polyhedral group by showing that the invariant polynomials of modular forms satisfy the polyhedral equations associated to Γ.

Original languageEnglish
Pages (from-to)285-319
Number of pages35
JournalCommunications in Mathematical Physics
Volume268
Issue number2
DOIs
Publication statusPublished - Dec 1 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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