Seifert cobordisms and the Chen-Yang volume conjecture

TL;DR

This paper investigates the asymptotic behavior of Turaev-Viro invariants for 3-manifolds with boundary, demonstrating the invariants' volume conjecture remains valid under Seifert-fibered gluing, and proves the conjecture for specific classes of 3-manifolds.

Contribution

It establishes the stability of the Turaev-Viro volume conjecture under Seifert-fibered gluings and proves it for all Seifert fibered and certain graph 3-manifolds.

Findings

Volume conjecture holds under Seifert-fibered gluings

Proves the conjecture for all Seifert fibered 3-manifolds with boundary

Validates the conjecture for large classes of graph 3-manifolds

Abstract

We study the large $r$ asymptotic behavior of the Turaev-Viro invariants $TV_r(M; e^{\frac{2\pi i}{r}})$ of 3-manifolds with toroidal boundary, under the operation of gluing a Seifert-fibered 3-manifold along a component of $\partial M$. 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.