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Indexed by:期刊论文

Date of Publication:2018-11-01

Journal:JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS

Included Journals:SCIE、Scopus

Volume:27

Issue:13,SI

ISSN No.: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.