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Unoriented Knot Floer Homology and the Unoriented Four-Ball Genus

Author(s): Ozsvath, Peter Steven; Stipsicz, Andras I.; Szabo, Zoltan

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Abstract: In an earlier work, we introduced a family tHFK(K) of t-modified knot Floer homologies, defined by modifying the construction of knot Floer homology HFK- (K). The resulting groups were then used to define concordance homomorphisms gamma(t) indexed by t is an element of [0, 2]. In the present work we elaborate on the special case t = 1, and call the corresponding modified knot Floer homology the unoriented knot Floer homology of K. The corresponding concordance homomorphism when t = 1 is denoted by nu. Using elementary methods (based on grid diagrams and normal forms for surface cobordisms), we show that. gives a lower bound for the smooth four-dimensional crosscap number of K-the minimal first Betti number of a smooth (possibly non-orientable) surface in D-4 that meets the boundary S-3 along the given knot K.
Publication Date: Sep-2017
Electronic Publication Date: 28-Jul-2016
Citation: Ozsvath, Peter S, Stipsicz, Andras I, Szabo, Zoltan. (2017). Unoriented Knot Floer Homology and the Unoriented Four-Ball Genus. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 5137 - 5181. doi:10.1093/imrn/rnw143
DOI: doi:10.1093/imrn/rnw143
ISSN: 1073-7928
EISSN: 1687-0247
Pages: 5137 - 5181
Type of Material: Journal Article
Version: Author's manuscript

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