Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology

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dc.creatorBaker, Kenneth L.
dc.creatorGrigsby, J. Elisenda
dc.creatorHedden, Matthew
dc.date2007-10-01
dc.date2008-08-04
dc.date.accessioned2026-07-07T09:54:07Z
dc.date.available2026-07-07T09:54:07Z
dc.descriptionSimilar to knots in S^3, any knot in a lens space has a grid diagram from which one can combinatorially compute all of its knot Floer homology invariants. We give an explicit description of the generators, differentials, and rational Maslov and Alexander gradings in terms of combinatorial data on the grid diagram. Motivated by existing results for the Floer homology of knots in S^3 and the similarity of the combinatorics presented here, we conjecture that a certain family of knots is characterized by their Floer homology. Coupled with work of the third author, an affirmative answer to this would prove the Berge conjecture, which catalogs the knots in S^3 admitting lens space surgeries.
dc.description27 pages, 8 figures; Expositional improvements, corrected normalization of A grading in proof of Lemma 4.10
dc.identifierhttps://arxiv.org/abs/0710.0359
dc.identifierhttp://arxiv.org/abs/0710.0359
dc.identifierInternational Mathematics Research Notices (2008) Vol. 2008 : article ID rnn024, 39 pages
dc.identifierdoi:10.1093/imrn/rnn024
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/166200
dc.subjectGeometric Topology
dc.subjectSymplectic Geometry
dc.subject57R58; 57M27
dc.titleGrid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
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