Knot concordance and von Neumann $ρ$-invariants
| dc.creator | Cochran, Tim D. | |
| dc.creator | Teichner, Peter | |
| dc.date | 2004-11-03 | |
| dc.date.accessioned | 2026-07-07T08:37:48Z | |
| dc.date.available | 2026-07-07T08:37:48Z | |
| dc.description | We prove the nontriviality, at all integral levels n, of the filtration, F_n, of the classical topological knot concordance group recently defined by the authors and Kent Orr [COT]. Recall that this filtration is significant not only because of it's strong connection to Whitney tower constructions of Casson and Freedman, but also because all previously-known concordance invariants are related to the first few terms in the filtration. In [COT] we proved nontriviality at the first new level (n=3) by using von Neumann $ρ$-invariants of the 3-manifolds obtained by zero surgery on the knots. Here, for larger n, we use the Cheeger-Gromov estimate for such $ρ$-invariants, as well as some rather involved algebraic arguments using our noncommutative Blanchfield forms. In addition, we consider a closely related filtration, defined in terms of Gropes in the 4-ball and show that this filtration is non-trivial for all n>2. | |
| dc.identifier | https://arxiv.org/abs/math/0411057 | |
| dc.identifier | http://arxiv.org/abs/math/0411057 | |
| dc.identifier | Duke Math. Journal, 137 (2007), no.2, 337-379 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140533 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M | |
| dc.title | Knot concordance and von Neumann $ρ$-invariants | |
| dc.type | text |