Slice knots with distinct Ozsvath-Szabo and Rasmussen Invariants
| dc.creator | Livingston, Charles | |
| dc.date | 2006-02-27 | |
| dc.date | 2006-03-11 | |
| dc.date.accessioned | 2026-07-07T10:10:44Z | |
| dc.date.available | 2026-07-07T10:10:44Z | |
| dc.description | 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. | |
| dc.description | In the first version of this note, the main result was applied to show that the smooth concordance group of topologically slice knots contains a summand isomorphic to a free abelian group on two generators. The author has learned that Manolescu and Owens previously found a knot invariant, based on the Heegaard-Floer Homology of the 2-fold branched cover of the knot, that they used to detect such a summand (see math.GT/0508065). Thus, a consequence of this note is that the work of Hedden-Ording and Manolescu-Owens combines to give a summand that is free on three generators | |
| dc.identifier | https://arxiv.org/abs/math/0602631 | |
| dc.identifier | http://arxiv.org/abs/math/0602631 | |
| dc.identifier | Proc. Amer. Math. Soc. 136 (2008) 347-349 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171679 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25 | |
| dc.title | Slice knots with distinct Ozsvath-Szabo and Rasmussen Invariants | |
| dc.type | text |