The strong slope conjecture for twisted generalized whitehead doubles

Kenneth L. Baker, Kimihiko Motegi, Toshie Takata

Research output: Contribution to journalArticlepeer-review

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 (US)
Pages (from-to)545-608
Number of pages64
JournalQuantum Topology
Volume11
Issue number3
DOIs
StatePublished - 2020

Keywords

  • Boundary slope
  • Colored Jones polynomial
  • Jones slope
  • Slope Conjecture
  • Strong Slope Conjecture
  • Whitehead double

ASJC Scopus subject areas

  • Mathematical Physics
  • Geometry and Topology

Fingerprint Dive into the research topics of 'The strong slope conjecture for twisted generalized whitehead doubles'. Together they form a unique fingerprint.

Cite this