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The Bonahon-Wong-Yang volume conjecture for the four-puncture sphere

Geometric Topology 2024-06-04 v2 Mathematical Physics math.MP Quantum Algebra

Abstract

We compute the Bonahon-Wong-Yang quantum invariant for self-diffeomorphisms of the four-puncture sphere explicitly, based on the representation theory of the Checkov-Fock algebra. As an application of the computation, we verify the volume conjecture proposed by Bonahon-Wong-Yang for the four puncture sphere bundles with some technical conditions. Together with the one-puncture torus bundles, this is the first family of examples for which the conjecture is verified providing evidence for the conjecture

Keywords

Cite

@article{arxiv.2311.13151,
  title  = {The Bonahon-Wong-Yang volume conjecture for the four-puncture sphere},
  author = {Tushar Pandey},
  journal= {arXiv preprint arXiv:2311.13151},
  year   = {2024}
}