Volume conjectures for the reshetikhin–turaev and the turaev–viro invariants

Qingtao Chen, Tian Yang

Research output: Contribution to journalArticle

Abstract

We consider the asymptotics of the Turaev–Viro and the Reshetikhin–Turaev invariants of a hyperbolic 3-manifold, evaluated at the root of unity exp(2π√-1/r) instead of the standard exp(2π√-1/r). We present evidence that, as r tends to ∞, these invariants grow exponentially with growth rates respectively given by the hyperbolic and the complex volume of the manifold. This reveals an asymptotic behavior that is different from that of Witten’s Asymptotic Expansion Conjecture, which predicts polynomial growth of these invariants when evaluated at the standard root of unity. This new phenomenon suggests that the Reshetikhin–Turaev invariants may have a geometric interpretation other than the original one via SU(2) Chern–Simons gauge theory.

Original languageEnglish (US)
Pages (from-to)419-460
Number of pages42
JournalQuantum Topology
Volume9
Issue number3
DOIs
StatePublished - Jan 1 2018

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Invariant
Roots of Unity
Hyperbolic 3-manifold
Chern-Simons Theories
Polynomial Growth
Gauge Theory
Asymptotic Expansion
Asymptotic Behavior
Tend
Predict
Standards
Evidence
Interpretation

Keywords

  • Reshetikhin-Turaev invariants
  • Turaev-Viro invariants
  • Volume conjecture

ASJC Scopus subject areas

  • Mathematical Physics
  • Geometry and Topology

Cite this

Volume conjectures for the reshetikhin–turaev and the turaev–viro invariants. / Chen, Qingtao; Yang, Tian.

In: Quantum Topology, Vol. 9, No. 3, 01.01.2018, p. 419-460.

Research output: Contribution to journalArticle

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