Slice knots with distinct Ozsvath-Szabo and Rasmussen Invariants

Charles Livingston

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arXiv · math/0602631

Slice knots with distinct Ozsvath-Szabo and Rasmussen Invariants

Charles Livingston

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Abstract

As proved by Hedden and Ording, there exist knots for which the Ozsvath-Szabo and Rasmussen smooth concordance invariants, tau and s, differ. The Hedden-Ording examples have nontrivial Alexander polynomials and are not topologically slice. It is shown in this note that a simple manipulation of the Hedden-Ording examples yields a topologically slice Alexander polynomial one knot for which tau and s differ. Manolescu and Owens have previously found a concordance invariant that is independent of both tau and s on knots of polynomial one, and as a consequence have shown that the smooth concordance group of topologically slice knots contains a summand isomorphic to a free abelian group on two generators. It thus follows quickly from the observation in this note that this concordance group contains a subgroup isomorphic to a free abelian group on three generators.

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Charles Livingston. 2006-03-11. Slice knots with distinct Ozsvath-Szabo and Rasmussen Invariants. https://arxiv.org/abs/math/0602631

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