Session S28 - Knots, Surfaces, 3-manifolds

Friday, July 23, 18:00 ~ 18:30 UTC-3

The Strong Slope Conjecture for Mazur pattern satellite knots

Kimihiko Motegi

Nihon University, Japan   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The Slope Conjecture proposed by Garoufalidis asserts that the degree of the colored Jones polynomial determines a boundary slope, and its refinement, the Strong Slope Conjecture proposed by Kalfagianni and Tran asserts that the linear term in the degree determines the topology of an essential surface that satisfies the Slope Conjecture. Under certain hypotheses, we show that a Mazur pattern satellite knots satisfy the Strong Slope Conjecture if the original knot does. Consequently, combining with previous results, any knot obtained by a finite sequence of cabling, connected sums, Whitehead doubling and taking Mazur pattern satellites of adequate knots (including alternating knots) or torus knots satisfies the Strong Slope Conjecture.

Joint work with Kenneth L. Baker (University of Miami) and Toshie Takata (Kyushu University).

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