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 areWhitehead doubles which are not adequate.
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Kenneth L. Baker, Kimihiko Motegi, Toshie Takata, The Strong Slope Conjecture for twisted generalized Whitehead doubles. Quantum Topol. 11 (2020), no. 3, pp. 545–608DOI 10.4171/QT/242