Turaev-Viro invariants, colored Jones polynomials, and volume Academic Article uri icon


  • European Mathematical Society. We obtain a formula for the TuraevViro invariants of a link complement in terms of values of the colored Jones polynomials of the link. As an application, we give the first examples of 3-manifolds where the large r asymptotics of the TuraevViro invariants determine the hyperbolic volume. We verify the volume conjecture of Chen and the third named author [7] for the figure-eight knot and the Borromean rings. Our calculations also exhibit new phenomena of asymptotic behavior of values of the colored Jones polynomials that seem to be predicted neither by the Kashaev-Murakami-Murakami volume conjecture and its generalizations nor by Zagiers quantum modularity conjecture. We conjecture that the asymptotics of the TuraevViro invariants of any link complement determine the simplicial volume of the link, and verify this conjecture for all knots with zero simplicial volume. Finally, we observe that our simplicial volume conjecture is compatible with connected summations and split unions of links.

published proceedings


author list (cited authors)

  • Detcherry, R., Kalfagianni, E., & Yang, T.

citation count

  • 12

complete list of authors

  • Detcherry, Renaud||Kalfagianni, Efstratia||Yang, Tian

publication date

  • January 2018