Concordance of knots in S-1 x S-2

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We establish a number of results about smooth and topological concordance of knots in S1xS2. The winding number of a knot in S1xS2 is defined to be its class in H1(S1xS2;Z)Z. We show that there is a unique smooth concordance class of knots with winding number one. This improves the corresponding result of Friedl-Nagel-Orson-Powell in the topological category. We say a knot in S1xS2 is slice (respectively, topologically slice) if it bounds a smooth (respectively, locally flat) disk in D2xS2. We show that there are infinitely many topological concordance classes of non-slice knots, and moreover, for any winding number other than +/- 1, there are infinitely many topological concordance classes even within the collection of slice knots. Additionally, we demonstrate the distinction between the smooth and topological categories by constructing infinite families of slice knots that are pairwise topologically but not smoothly concordant, as well as non-slice knots that are topologically slice and are pairwise topologically, but not smoothly, concordant.
Publisher
WILEY
Issue Date
2018-08
Language
English
Article Type
Article
Citation

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, v.98, pp.59 - 84

ISSN
0024-6107
DOI
10.1112/jlms.12125
URI
http://hdl.handle.net/10203/280216
Appears in Collection
MA-Journal Papers(저널논문)
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