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论文类型：期刊论文

发表时间：2018-11-01

发表刊物：JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS

收录刊物：SCIE、Scopus

卷号：27

期号：13,SI

ISSN号：0218-2165

关键字：Slope conjecture; colored Jones polynomial; quadratic integer programming; boundary slope; incompressible surface

摘要：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.