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Seifert cobordisms and the Chen-Yang volume conjecture (2505.01546v1)
Published 2 May 2025 in math.GT and math.QA
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.