Journal of the Mathematical Society of Japan

The strong slope conjecture and torus knots

Efstratia KALFAGIANNI

Advance publication

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Abstract

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.

Note

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

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1558425754

Digital Object Identifier
doi:10.2969/jmsj/81068106

Subjects
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]

Keywords
boundary slope Jones slope strong slope conjecture torus knots

Citation

KALFAGIANNI, Efstratia. The strong slope conjecture and torus knots. J. Math. Soc. Japan, advance publication, 21 May 2019. doi:10.2969/jmsj/81068106. https://projecteuclid.org/euclid.jmsj/1558425754


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