A concordance invariant from the Floer homology of double branched covers

Manolescu, C. and Owens, B. (2007) A concordance invariant from the Floer homology of double branched covers. International Mathematics Research Notices, 2007, (doi:10.1093/imrn/rnm077)

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Publisher's URL: http://imrn.oxfordjournals.org/content/2007/rnm077.short

Abstract

Ozsváth and Szabó defined an analog of the Frøyshov invariant in the form of a correction term for the grading in Heegaard Floer homology. Applying this to the double cover of the 3-sphere branched over a knot K, we obtain an invariant δ of knot concordance. We show that δ is determined by the signature for alternating knots and knots with up to nine crossings, and conjecture a similar relation for all H-thin knots. We also use δ to prove that for all knots K with τ(K) > 0, the positive untwisted double of K is not smoothly slice.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Owens, Dr Brendan
Authors: Manolescu, C., and Owens, B.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:International Mathematics Research Notices
ISSN:1073-7928

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