Quadratic integer programming and the Slope Conjecture

被引：0

作者：

Garoufalidis, Stavros ^{[1
]}

van der Veen, Roland ^{[2
]}

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[2] Leiden Univ, Inst Math, Niels Bohrweg 1, Leiden, Netherlands

来源：

NEW YORK JOURNAL OF MATHEMATICS | 2016年 / 22卷

基金：

美国国家科学基金会;

关键词：

knot; link; Jones polynomial; Jones slope; quasi-polynomial; pretzel knots; fusion; fusion number of a knot; polytopes; incompressible surfaces; slope; tropicalization; state sums; tight state sums; almost tight state sums; regular ideal octahedron; quadratic integer programming; VOLUME CONJECTURE; BOUNDARY SLOPES; INCOMPRESSIBILITY; INVARIANTS; CURVES; KNOTS; LINKS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Slope Conjecture relates a quantum knot invariant, (the degree of the colored Jones polynomial of a knot) with a classical one (boundary slopes of incompressible surfaces in the knot complement). The degree of the colored Jones polynomial can be computed by a suitable (almost tight) state sum and the solution of a corresponding quadratic integer programming problem. We illustrate this principle for a 2-parameter family of 2-fusion knots. Combined with the results of Dunfield and the first author, this confirms the Slope Conjecture for the 2-fusion knots of one sector.

引用

页码：907 / 932

页数：26

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