Publications [#328057] of Adam S. Levine

Papers Published

1. Baldwin, JA; Levine, AS; Sarkar, S, Khovanov homology and knot Floer homology for pointed links, Journal of Knot Theory and Its Ramifications, vol. 26 no. 2 (February, 2017), pp. 1740004-1740004, World Scientific Pub Co Pte Lt [doi]
   (last updated on 2026/02/08)

   Abstract:
   A well-known conjecture states that for any l-component link L in S3, the rank of the knot Floer homology of L (over any field) is less than or equal to 2l-1 times the rank of the reduced Khovanov homology of L. In this paper, we describe a framework that might be used to prove this conjecture. We construct a modified version of Khovanov homology for links with multiple basepoints and show that it mimics the behavior of knot Floer homology. We also introduce a new spectral sequence converging to knot Floer homology whose E1 page is conjecturally isomorphic to our new version of Khovanov homology; this would prove that the conjecture stated above holds over the field Z2.