Geodesic
Knot Floer homology in cyclic branched covers
Grigsby, J Elisenda1
1Evans Hall, University of California, Berkeley, Berkeley, CA 94720, USA
Algebraic and Geometric Topology, Tome 6 (2006) no. 3, pp. 1355-1398
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In this paper, we introduce a sequence of invariants of a knot K in S3: the knot Floer homology groups HFK̂(Σm(K);K˜,i) of the preimage of K in the m–fold cyclic branched cover over K. We exhibit HFK̂(Σm(K);K˜,i) as the categorification of a well-defined multiple of the Turaev torsion of Σm(K) −K˜ in the case where Σm(K) is a rational homology sphere. In addition, when K is a two-bridge knot, we prove that HFK̂(Σ2(K);K˜,s0)≅HFK̂(S3;K) for s0 the spin Spinc structure on Σ2(K). We conclude with a calculation involving two knots with identical HFK̂(S3;K,i) for which HFK̂(Σ2(K);K˜,i) differ as ℤ2–graded groups.

DOI : 10.2140/agt.2006.6.1355
Keywords: Heegaard Floer homology, branched covers

Grigsby, J Elisenda  1

1 Evans Hall, University of California, Berkeley, Berkeley, CA 94720, USA 
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Grigsby, J Elisenda. Knot Floer homology in cyclic branched covers. Algebraic and Geometric Topology, Tome 6 (2006) no. 3, pp. 1355-1398. doi: 10.2140/agt.2006.6.1355

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