Turaev-Viro invariants of links and the colored Jones polynomial

Geometry Topology Seminar
Wednesday, January 25, 2017 - 15:05
1 hour (actually 50 minutes)
Skiles 006
Michigan State University
In a recent conjecture by Tian Yang and Qingtao Chen, it has been observedthat the log of Turaev-Viro invariants of 3-manifolds  at a special root ofunity grow  proportionnally to the level times hyperbolic volume of themanifold, as in the usual volume conjecture for the colored Jonespolynomial.In the case of link complements, we derive a formula to expressTuraev-Viro invariants as a sum of values of colored Jones polynomial, andget a proof of Yang and Chen's conjecture for a few link complements. Theformula also raises new questions about the asymptotics of colored Jonespolynomials. Joint with Effie Kalfagianni and Tian Yang.