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The Bonahon-Wong-Yang volume conjecture for the four-puncture sphere (2311.13151v2)
Published 22 Nov 2023 in math.GT, math-ph, math.MP, and math.QA
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
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