Knot Floer homology in cyclic branched covers

Details Knot Floer homology in cyclic branched covers Knot Floer homology in cyclic branched covers

2005-07-25

arxiv.org/abs/math/0507498v3

Algebr. Geom. Topol. 6 (2006) 1355-1398

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 25 September 2006

Scientific paper

10.2140/agt.2006.6.1355

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.

Affiliated with

Also associated with

No associations

Rating

Knot Floer homology in cyclic branched covers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Knot Floer homology in cyclic branched covers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Knot Floer homology in cyclic branched covers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-53247