Department of Mathematics

Geometry and Topology

  •  Ka Ho Wong, Texas A&M University
  •  Asymptotics of the relative Reshetikhin-Turaev invariants
  •  10/12/2021
  •  4:00 PM - 5:00 PM
  •  Online (virtual meeting) (Virtual Meeting Link)
  •  Honghao Gao (gaohongh@msu.edu)

In a series of joint works with Tian Yang, we made a volume conjecture and an asymptotic expansion conjecture for the relative Reshetikhin-Turaev invariants for a closed oriented 3-manifold with a colored framed link inside it. We propose that their asymptotic behavior is related to the volume, the Chern-Simons invariant and the adjoint twisted Reidemeister torsion associated with the hyperbolic cone metric on the manifold with singular locus the link and cone angles determined by the coloring. In this talk, I will first discuss how our volume conjecture can be understood as an interpolation between the Kashaev-Murakami-Murakami volume conjecture of the colored Jones polynomials and the Chen-Yang volume conjecture of the Reshetikhin-Turaev invariants. Then I will describe how the adjoint twisted Reidemeister torsion shows up in the asymptotic expansion of the invariants. Especially, we find new explicit formulas for the adjoint twisted Reidemeister torsion for the fundamental shadow link complements and for the 3-manifold obtained by doing hyperbolic Dehn-filling on those link complements. Those formulas cover a very large class of hyperbolic 3-manifold and appear naturally in the asymptotic expansion of quantum invariants. Finally, I will summarize the recent progress of the asymptotic expansion conjecture of the fundamental shadow link pairs.

 

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