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2006 Knot Floer homology in cyclic branched covers
J Elisenda Grigsby
Algebr. Geom. Topol. 6(3): 1355-1398 (2006). DOI: 10.2140/agt.2006.6.1355

Abstract

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 2–graded groups.

Citation

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J Elisenda Grigsby. "Knot Floer homology in cyclic branched covers." Algebr. Geom. Topol. 6 (3) 1355 - 1398, 2006. https://doi.org/10.2140/agt.2006.6.1355

Information

Received: 9 September 2005; Accepted: 10 June 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1133.57006
MathSciNet: MR2253451
Digital Object Identifier: 10.2140/agt.2006.6.1355

Subjects:
Primary: 57M27, 57R58
Secondary: 57M05

Rights: Copyright © 2006 Mathematical Sciences Publishers

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