Journal of the Mathematical Society of Japan

The strong slope conjecture and torus knots


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We show that the strong slope conjecture implies that the degree of the colored Jones polynomial detects all torus knots. As an application we obtain that an adequate knot that has the same colored Jones polynomial degrees as a torus knot must be a $(2,q)$-torus knot.


The author was supported in part by NSF grant DMS-1708249.

Article information

J. Math. Soc. Japan, Advance publication (2019), 7 pages.

Received: 12 August 2018
Revised: 26 August 2018
First available in Project Euclid: 21 May 2019

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Digital Object Identifier

Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M50: Geometric structures on low-dimensional manifolds 57N10: Topology of general 3-manifolds [See also 57Mxx]

boundary slope Jones slope strong slope conjecture torus knots


KALFAGIANNI, Efstratia. The strong slope conjecture and torus knots. J. Math. Soc. Japan, advance publication, 21 May 2019. doi:10.2969/jmsj/81068106.

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