Topologically slice knots of smooth concordance order two

Matthew Hedden; Se-Goo Kim; Charles Livingston

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arXiv · 1212.6628

Topologically slice knots of smooth concordance order two

Matthew Hedden·Se-Goo Kim·Charles Livingston

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Abstract

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 4-manifolds. Here, as an application of Ozsvath and Szabo'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. 2012-12-29. Topologically slice knots of smooth concordance order two. https://arxiv.org/abs/1212.6628

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