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2 results

  • Link Floer Homology Categorifies the Conway Function

  • Part of
  • Mounir Benheddi, David Cimasoni
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 59 / Issue 4 / November 2016
    Published online by Cambridge University Press:
    18 January 2016, pp. 813-836

  • 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.

  • THE CONWAY FUNCTION OF A SPLICE

  • David Cimasoni
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 48 / Issue 1 / February 2005
    Published online by Cambridge University Press:
    15 February 2005, pp. 61-73
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  • We give a closed formula for the Conway function of a splice in terms of the Conway function of its splice components. As corollaries, we refine and generalize results of Seifert, Torres and Sumners-Woods.

    AMS 2000 Mathematics subject classification: Primary 57M25