Oliver T. Dasbach

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The colored Jones polynomial is a function JK : N −→ Z[t, t] associated with a knot K in 3-space. We will show that for an alternating knot K the absolute values of the first and the last three leading coefficients of JK(n) are independent of n when n is sufficiently large. Computation of sample knots indicates that this should be true for any fixed leading(More)
The Jones polynomial of an alternating link is a certain specialization of the Tutte polynomial of the (planar) checkerboard graph associated to an alternating projection of the link. The Bollobás–Riordan– Tutte polynomial generalizes the Tutte polynomial of graphs to graphs that are embedded in closed oriented surfaces of higher genus. In this paper we(More)
Khovanov homology is a bigraded Z-module that categorifies the Jones polynomial. The support of Khovanov homology lies on a finite number of slope two lines with respect to the bigrading. The Khovanov width is essentially the largest horizontal distance between two such lines. We show that it is possible to generate infinite families of links with the same(More)