# The strong slope conjecture for twisted generalized whitehead doubles

Kenneth L. Baker, Kimihiko Motegi, Toshie Takata

2 被引用数 (Scopus)

## 抄録

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 twisted, generalized Whitehead doubles of a knot satisfies the Slope Conjecture and the Strong Slope Conjecture if the original knot does. Additionally, we provide a proof that there are Whitehead doubles which are not adequate.

本文言語 英語 545-608 64 Quantum Topology 11 3 https://doi.org/10.4171/QT/242 出版済み - 2020

• 数理物理学
• 幾何学とトポロジー

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