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Link Floer Homology Categorifies the Conway Function
Published online by Cambridge University Press: 18 January 2016
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.
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- 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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