Open Access
March 2016 Topologically slice knots of smooth concordance order two
Matthew Hedden, Se-Goo Kim, Charles Livingston
J. Differential Geom. 102(3): 353-393 (March 2016). DOI: 10.4310/jdg/1456754013


The existence of topologically slice knots that are of infinite order in the knot concordance group followed from Freedman’s work on topological surgery and Donaldson’s gauge theoretic approach to four-manifolds. Here, as an application of Ozsváth and Szabó’s Heegaard Floer theory, we show the existence of an infinite subgroup of the smooth concordance group generated by topologically slice knots of concordance order two. In addition, no nontrivial element in this subgroup can be represented by a knot with Alexander polynomial one.


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Matthew Hedden. Se-Goo Kim. Charles Livingston. "Topologically slice knots of smooth concordance order two." J. Differential Geom. 102 (3) 353 - 393, March 2016.


Published: March 2016
First available in Project Euclid: 29 February 2016

zbMATH: 1339.57011
MathSciNet: MR3466802
Digital Object Identifier: 10.4310/jdg/1456754013

Rights: Copyright © 2016 Lehigh University

Vol.102 • No. 3 • March 2016
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