Knot Floer homology in cyclic branched covers
Abstract
In this paper, we introduce a sequence of invariants of a knot K in S^3: the knot Floer homology groups of the preimage of K in the m-fold cyclic branched cover over K. We exhibit the knot Floer homology in the m-fold branched cover as the categorification of a multiple of the Turaev torsion in the case where the m-fold branched cover is a rational homology sphere. In addition, when K is a 2-bridge knot, we prove that the knot Floer homology of the lifted knot in a particular Spin^c structure in the branched double cover matches the knot Floer homology of the original knot K in S^3. We conclude with a calculation involving two knots with identical knot Floer homology in S^3 for which the knot Floer homology groups in the double branched cover differ as Z_2-graded groups.
Cite
@article{arxiv.math/0507498,
title = {Knot Floer homology in cyclic branched covers},
author = {J Elisenda Grigsby},
journal= {arXiv preprint arXiv:math/0507498},
year = {2009}
}
Comments
This is the version published by Algebraic & Geometric Topology on 25 September 2006