Release Time:2019-03-13  Hits:

Indexed by: Journal Article

Date of Publication: 2018-11-01

Journal: JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS

Included Journals: Scopus、SCIE

Volume: 27

Issue: 13,SI

ISSN: 0218-2165

Key Words: Slope conjecture; colored Jones polynomial; quadratic integer programming; boundary slope; incompressible surface

Abstract: The Slope Conjecture and the Strong Slope Conjecture predict that the degree of the colored Jones polynomial of a knot is matched by the boundary slope and the Euler characteristic of some essential surfaces in the knot complement. By solving a problem of quadratic integer programming to find the maximal degree and using the Hatcher-Oertel edgepath system to find the corresponding essential surface, we verify the Slope Conjectures for a family of 3-string Montesinos knots satisfying certain conditions.