Genus two mutant knots with the same dimension in knot Floer and Khovanov homologies
Geometric Topology
2015-05-27 v4
Abstract
We exhibit an infinite family of knots with isomorphic knot Heegaard Floer homology. Each knot in this infinite family admits a nontrivial genus two mutant which shares the same total dimension in both knot Floer homology and Khovanov homology. Each knot is distinguished from its genus two mutant by both knot Floer homology and Khovanov homology as bigraded groups. Additionally, for both knot Heegaard Floer homology and Khovanov homology, the genus two mutation interchanges the groups in -gradings and .
Keywords
Cite
@article{arxiv.1204.2524,
title = {Genus two mutant knots with the same dimension in knot Floer and Khovanov homologies},
author = {Allison Moore and Laura Starkston},
journal= {arXiv preprint arXiv:1204.2524},
year = {2015}
}
Comments
Information about $\delta$-graded homology has been changed along with statement of Theorem 1 and Table 1. Significant changes to Section 3