Knot concordance, Whitney towers and L^2 signatures
| dc.creator | Cochran, Tim D. | |
| dc.creator | Orr, Kent E. | |
| dc.creator | Teichner, Peter | |
| dc.date | 1999-08-22 | |
| dc.date | 2004-02-09 | |
| dc.date.accessioned | 2026-07-07T05:30:26Z | |
| dc.date.available | 2026-07-07T05:30:26Z | |
| dc.description | We construct many examples of non-slice knots in 3-space that cannot be distinguished from slice knots by previously known invariants. Using Whitney towers in place of embedded disks, we define a geometric filtration of the 3-dimensional topological knot concordance group. The bottom part of the filtration exhibits all classical concordance invariants, including the Casson-Gordon invariants. As a first step, we construct an infinite sequence of new obstructions that vanish on slice knots. These take values in the L-theory of skew fields associated to certain {\em universal} groups. Finally, we use the dimension theory of von Neumann algebras to define an L^2 signature and use this to detect the first unknown step in our obstruction theory. | |
| dc.description | 87 pages published version | |
| dc.identifier | https://arxiv.org/abs/math/9908117 | |
| dc.identifier | http://arxiv.org/abs/math/9908117 | |
| dc.identifier | Ann. of Math. (2), Vol. 157 (2003), no. 2, 433--519 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78992 | |
| dc.subject | Geometric Topology | |
| dc.title | Knot concordance, Whitney towers and L^2 signatures | |
| dc.type | text |