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, Professor 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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