An expression for the Homflypt polynomial and some applications

David Emmes

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arXiv · 1009.5056

An expression for the Homflypt polynomial and some applications

David Emmes

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Abstract

Associated with each oriented link is the two variable Homflypt polynomial. The Morton-Franks-Williams (MFW) inequality gives rise to an expression for the Homflypt polynomial with MFW coefficient polynomials. These MFW coefficient polynomials are labelled in a braid-dependent manner and may be zero, but display a number of interesting relations. One consequence is an expression for the first three Laurent coefficient polynomials in z as a function of the other coefficient polynomials and three link invariants: the minimum v-degree and v-span of the Homflypt polynomial, and the Conway polynomial. These expressions are used to derive additional properties of the Homflypt polynomial for general n-braid links. One specific result is that the Jones and Homflypt polynomials distinguish the same three-braid links.

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David Emmes. 2014-01-04. An expression for the Homflypt polynomial and some applications. https://arxiv.org/abs/1009.5056

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