Seifert cobordisms and the Chen-Yang volume conjecture

2025/05/02 by Detcherry, Renaud, Kalfagianni, Efstratia, Marasinghe, Shashini
#57K16 #57K31 #57M2 #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2505.01546

Abstract

We study the large r asymptotic behavior of the Turaev-Viro invariants TV_r(M; e^(2πi)/(r)) of 3-manifolds with toroidal boundary, under the operation of gluing a Seifert-fibered 3-manifold along a component of ∂ M. We show that the Turaev-Viro invariants volume conjecture is closed under this operation. As an application we prove the volume conjecture for all Seifert fibered 3-manifolds with boundary and for large classes of graph 3-manifolds.

Citations

• Seifert fibered 3-manifolds and Turaev-Viro invariants volume conjecture
• Turaev-Viro invariants and cabling operations
• Asymptotic additivity of the Turaev-Viro invariants for a family of 3-manifolds
• Relative Reshetikhin-Turaev invariants, hyperbolic cone metrics and discrete Fourier transforms I
• An upper bound conjecture for the Yokota invariant
• Asymptotics of some quantum invariants of the Whitehead chains
• Growth of quantum 6j-symbols and applications to the Volume Conjecture
• Quantum representations and monodromies of fibered links
• Gromov norm and Turaev-Viro invariants of 3-manifolds
• Turaev-Viro invariants, colored Jones polynomials and volume
• Volume conjectures for the Reshetikhin-Turaev and the Turaev-Viro invariants
• Invariants of 3-manifolds via link polynomials and quantum groups

Related

• Seifert fibered 3-manifolds and Turaev-Viro invariants volume conjecture
• Asymptotic additivity of the Turaev-Viro invariants for a family of 3-manifolds
• The Chen-Yang volume conjecture for knots in handlebodies
• A relative version of the Turaev-Viro invariants and the volume of hyperbolic polyhedral 3-manifolds
• Growth of Turaev-Viro invariants and cabling