The strong slope conjecture for twisted generalized whitehead doubles

Kenneth L. Baker, Kimihiko Motegi, Toshie Takata

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)545-608
    Number of pages64
    JournalQuantum Topology
    Volume11
    Issue number3
    DOIs
    Publication statusPublished - 2020

    All Science Journal Classification (ASJC) codes

    • Mathematical Physics
    • Geometry and Topology

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