The Teichmüller TQFT Volume Conjecture for twist knots
(2019) Comptes rendus - Mathématique — Vol. 357, n° 3, p. 299-305 (2019)
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- Abstract
- The Teichmüller TQFT, defined by Andersen and Kashaev, gives rise to a quantum invariant of triangulated hyperbolic knot complements; it has an associated volume conjecture, where the hyperbolic volume of the knot appears as a certain asymptotic coefficient. In this note, we announce a proof of this volume conjecture for all twist knots up to 14 crossings; along the way we explicitly compute the partition function of the Teichmüller TQFT for the whole infinite family of twist knots. Among other tools, we use an algorithm of Thurston to construct a convenient ideal triangulation of a twist knot complement, as well as the saddle point method for computing limits of complex integrals with parameters.
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Citations
Ben Aribi, F., & Eiichi Piguet-Nakazawa. (2019). The Teichmüller TQFT Volume Conjecture for twist knots. Comptes rendus - Mathématique, 357(3), 299-305. https://doi.org/10.1016/j.crma.2019.02.004 (Original work published 2019)