New York Journal of Mathematics
Volume 27 (2021), 676-704


Kenneth L. Baker, Kimihiko Motegi, and Toshie Takata

The Strong Slope Conjecture for cablings and connected sums

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Published: April 25, 2021.
Keywords: colored Jones polynomial, Jones slope, boundary slope, slope conjecture, strong slope conjecture, cabling, connected sum, graph knot.
Subject: Primary 57M25, 57M27.

We show that, under some technical conditions, the Strong Slope Conjecture proposed by Kalfagianni and Tran is closed under connect sums and cabling. As an application, we establish the Strong Slope Conjecture for graph knots.


KLB was partially supported by a grant from the Simons Foundation (#523883 to Kenneth L. Baker). KM was partially supported by JSPS KAKENHI Grant Number 19K03502 and Joint Research Grant of Institute of Natural Sciences at Nihon University for 2019. TT was partially supported by JSPS KAKENHI Grant Number 17K05256.

Author information

Kenneth L. Baker:
Department of Mathematics
University of Miami
Coral Gables, FL 33146, USA


Kimihiko Motegi:
Department of Mathematics
Nihon University
3-25-40 Sakurajosui, Setagaya-ku, Tokyo 156--8550, Japan


Toshie Takata:
Graduate School of Mathematics
Kyushu University
744 Motooka, Nishi-ku, Fukuoka 819--0395, Japan