Seifert fibered 3-manifolds and Turaev-Viro invariants volume conjecture

Shashini Marasinghe

Seifert fibered 3-manifolds and Turaev-Viro invariants volume conjecture

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arxiv 2504.10682 v2 pith:UI6EYV2F submitted 2025-04-14 math.GT math.QA

Shashini Marasinghe This is my paper · ORCID

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keywords fiberedmanifoldsseifertconjectureinvariantslargeorientedturaev-viro

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abstract

We study the large $r$ asymptotic behaviour of the Turaev-Viro invariants of oriented Seifert fibered 3-manifolds at the root $q=e^\frac{2\pi i}{r}$. As an application, we prove the volume conjecture for large families of oriented Seifert fibered 3-manifolds with empty and non-empty boundary.

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Seifert cobordisms and the Chen-Yang volume conjecture
math.GT 2025-05 conditional novelty 7.0 of 10

Gluing a Seifert-fibered 3-manifold to a boundary torus preserves the growth rate of Turaev-Viro invariants, proving the volume conjecture for all Seifert fibered 3-manifolds with boundary and for classes of graph manifolds.

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