Constructions of $q$-hyperbolic knots

Efstratia Kalfagianni; Joseph M. Melby

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arXiv · 2304.00682

Constructions of $q$-hyperbolic knots

Efstratia Kalfagianni·Joseph M. Melby

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Abstract

We use Dehn surgery methods to construct infinite families of hyperbolic knots in the 3-sphere satisfying a weak form of the Turaev--Viro invariants volume conjecture. The results have applications to a conjecture of Andersen, Masbaum, and Ueno about quantum representations of surface mapping class groups. We obtain an explicit family of pseudo-Anosov mapping classes acting on surfaces of any genus and with one boundary component that satisfy the conjecture.

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BibTeX RIS

Efstratia Kalfagianni, Joseph M. Melby. 2023-04-03. Constructions of $q$-hyperbolic knots. https://arxiv.org/abs/2304.00682

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