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Link Floer Homology Categorifies the Conway Function

Part of: Low-dimensional topology

Published online by Cambridge University Press:  18 January 2016

Mounir Benheddi  and
David Cimasoni
Mounir Benheddi
Affiliation:
Université de Genève, Section de Mathématiques, 2–4 rue du Lièvre, 1211 Genève 4, Switzerland (mounir.benheddi@unige.ch; david.cimasoni@unige.ch)
David Cimasoni
Affiliation:
Université de Genève, Section de Mathématiques, 2–4 rue du Lièvre, 1211 Genève 4, Switzerland (mounir.benheddi@unige.ch; david.cimasoni@unige.ch)
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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 multi-variable Alexander polynomial, an invariant only defined up to a sign and powers of the variables. In this paper we remove this ambiguity by proving that this Euler characteristic is equal to the so-called Conway function, the representative of the multi-variable 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.

Keywords

Alexander polynomialConway functionlink Floer homologygrid diagram

MSC classification

Secondary: 57M25: Knots and links in $S^3$
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 4 , November 2016 , pp. 813 - 836
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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