Knot Floer homology in cyclic branched covers

dc.creatorGrigsby, J Elisenda
dc.date2005-07-25
dc.date2009-04-23
dc.date.accessioned2026-07-07T13:07:22Z
dc.date.available2026-07-07T13:07:22Z
dc.descriptionIn 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.
dc.descriptionThis is the version published by Algebraic & Geometric Topology on 25 September 2006
dc.identifierhttps://arxiv.org/abs/math/0507498
dc.identifierhttp://arxiv.org/abs/math/0507498
dc.identifierAlgebr. Geom. Topol. 6 (2006) 1355-1398
dc.identifierdoi:10.2140/agt.2006.6.1355
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228070
dc.subjectGeometric Topology
dc.subject57M27, 57R58, 57M05
dc.titleKnot Floer homology in cyclic branched covers
dc.typetext

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