Abstract
In this paper, we study the variation of the Turaev–Viro invariants for [Formula: see text]-manifolds with toroidal boundary under the operation of attaching a [Formula: see text]-cable space. We apply our results to a conjecture of Chen and Yang which relates the asymptotics of the Turaev–Viro invariants to the simplicial volume of a compact oriented [Formula: see text]-manifold. For [Formula: see text] and [Formula: see text] coprime, we show that the Chen–Yang volume conjecture is stable under [Formula: see text]-cabling. We achieve our results by studying the linear operator [Formula: see text] associated to the torus knot cable spaces by the Reshetikhin–Turaev [Formula: see text]-Topological Quantum Field Theory (TQFT), where the TQFT is well-known to be closely related to the desired Turaev–Viro invariants. In particular, our utilized method relies on the invertibility of the linear operator for which we provide necessary and sufficient conditions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.