Topologically slice knots of smooth concordance order two

By M. Hedden, Se-Goo Kim, Charles Livingston. 2012

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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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3d9721b7e80dff98dbb787af75d9e4aa74dc9fd2

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In Computational Theory and Mathematics

In Geometry and Topology

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A survey on Heegaard Floer homology and concordance (2015, methodology): “lex of J together with [NW10, Proposition 1.6] to compute δpn(K); see, for example, [HLR12] and [Jab12]. Moreover, similar techniques can be employed when the branched cover is surgery on a link; see [HKL12]. Alternatively, if Σpn(K) can be described as the boundary of a negative deﬁnite plumbing, t”