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Remarks on Jones Slopes and Surfaces of Knots

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Abstract

We show that the strong slope conjecture implies that the degrees of the colored Jones knot polynomials detect the figure 8 knot. Furthermore, we propose a characterization of alternating knots in terms of the Jones period and the degree span of the colored Jones polynomial

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Acknowledgments

The author thanks Christine Lee for useful conversations and in particular for help with Proposition 4.8. This material is based on research supported by NSF grants DMS-1708249 and DMS-2004155 and by a grant from the Institute for Advanced Study School of Mathematics.

Funding

This research is partially supported by NSF grants DMS-1708249 and DMS-2004155.

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  1. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA

    Efstratia Kalfagianni

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  1. Efstratia Kalfagianni
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Correspondence to Efstratia Kalfagianni.

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Kalfagianni, E. Remarks on Jones Slopes and Surfaces of Knots. Acta Math Vietnam 46, 289–299 (2021). https://doi.org/10.1007/s40306-020-00400-3

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