Publication: Non-semisimple invariants and Habiro series
Non-semisimple invariants and Habiro series
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Beliakova, A., & Hikami, K. (2021). Non-semisimple invariants and Habiro series. In A. Papadopoulos (Ed.), Topology and Geometry : A Collection of Essays Dedicated to Vladimir G. Turaev (pp. 161–174). EMS Publishing House. https://doi.org/10.4171/IRMA/33
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In this paper we establish an explicit relationship between Habiro’s cyclotomic expansion of the colored Jones polynomial (evaluated at a pth root of unity) and the Akutsu- Deguchi-Ohtsuki (ADO) invariants of the double twist knots. This allows us to compare the Witten-Reshetikhin-Turaev (WRT) and Costantino-Geer-Patureau (CGP) invariants of 3-manifolds obtained by 0-surgery on these knots. The difference between them is determined by the p − 1 coefficient of the Habiro series. We expect these to hold for all Seifert genus 1 knots.
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Beliakova, A., & Hikami, K. (2021). Non-semisimple invariants and Habiro series. In A. Papadopoulos (Ed.), Topology and Geometry : A Collection of Essays Dedicated to Vladimir G. Turaev (pp. 161–174). EMS Publishing House. https://doi.org/10.4171/IRMA/33