Quadratic integer programming and the slope conjecture

Stavros Garoufalidis; Roland van der Veen

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arXiv · 1405.5088

Quadratic integer programming and the slope conjecture

Stavros Garoufalidis·Roland van der Veen

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Abstract

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.

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Stavros Garoufalidis, Roland van der Veen. 2014-05-20. Quadratic integer programming and the slope conjecture. https://arxiv.org/abs/1405.5088

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