Link Floer homology categorifies the Conway function

Mounir Benheddi; David Cimasoni

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arXiv · 1408.3517

Link Floer homology categorifies the Conway function

Mounir Benheddi·David Cimasoni

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Abstract

Given an oriented link in the 3-sphere, the Euler characteristic of its link Floer homology is known to coincide with its multivariate Alexander polynomial, an invariant only defined up to a sign and powers of the variables. In this paper, we get rid of this ambiguity by proving that this Euler characteristic is equal to the so-called Conway function, the representative of the multivariate Alexander polynomial introduced by Conway in 1970 and explicitly constructed by Hartley in 1983. This is achieved by creating a model of the Conway function adapted to rectangular diagrams, which is then compared to the Euler characteristic of the combinatorial version of link Floer homology.

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BibTeX RIS

Mounir Benheddi, David Cimasoni. 2014-08-15. Link Floer homology categorifies the Conway function. https://arxiv.org/abs/1408.3517

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