New obstructions to doubly slicing knots
| dc.creator | Kim, Taehee | |
| dc.date | 2004-11-06 | |
| dc.date.accessioned | 2026-07-07T05:14:01Z | |
| dc.date.available | 2026-07-07T05:14:01Z | |
| dc.description | A knot in the 3-sphere is called doubly slice if it is a slice of an unknotted 2-sphere in the 4-sphere. We give a bi-sequence of new obstructions for a knot being doubly slice. We construct it following the idea of Cochran-Orr-Teichner's filtration of the classical knot concordance group. This yields a bi-filtration of the monoid of knots (under the connected sum operation) indexed by pairs of half integers. Doubly slice knots lie in the intersection of this bi-filtration. We construct examples of knots which illustrate non-triviality of this bi-filtration at all levels. In particular, these are new examples of algebraically doubly slice knots that are not doubly slice, and many of these knots are slice. Cheeger-Gromov's von Neumann rho invariants play a key role to show non-triviality of this bi-filtration. We also show that some classical invariants are reflected at the initial levels of this bi-filtration, and obtain a bi-filtration of the double concordance group. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/0411126 | |
| dc.identifier | http://arxiv.org/abs/math/0411126 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73121 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25 (Primary) 57M27, 57Q60 (Secondary) | |
| dc.title | New obstructions to doubly slicing knots | |
| dc.type | text |