Volume conjectures for the Reshetikhin-Turaev and the Turaev-Viro invariants Academic Article

abstract

• European Mathematical Society. We consider the asymptotics of the TuraevViro and the ReshetikhinTuraev invariants of a hyperbolic 3-manifold, evaluated at the root of unity exp(2-1/r) instead of the standard exp(2-1/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 Wittens Asymptotic Expansion Conjecture, which predicts polynomial growth of these invariants when evaluated at the standard root of unity. This new phenomenon suggests that the ReshetikhinTuraev invariants may have a geometric interpretation other than the original one via SU(2) ChernSimons gauge theory.

authors

• Yang, Tian

published proceedings

• QUANTUM TOPOLOGY

altmetric score

• 3

author list (cited authors)

• Chen, Q., & Yang, T.

citation count

• 15

complete list of authors

• Chen, Qingtao||Yang, Tian

publication date

• January 2018

publisher

• European Mathematical Society - EMS - Publishing House GmbH  Publisher

published in

• Quantum Topology  Journal

keywords

• Reshetikhin-turaev Invariants
• Turaev-viro Invariants
• Volume Conjecture

Digital Object Identifier (DOI)

• 10.4171/QT/111

start page

• 419

end page

• 460

volume

• 9

issue

• 3

URL

• http://dx.doi.org/10.4171/qt/111