Covering link calculus and iterated Bing doubles
| dc.creator | Cha, Jae Choon | |
| dc.creator | Kim, Taehee | |
| dc.date | 2007-12-21 | |
| dc.date | 2008-07-01 | |
| dc.date.accessioned | 2026-07-07T09:47:16Z | |
| dc.date.available | 2026-07-07T09:47:16Z | |
| dc.description | We give a new geometric obstruction to the iterated Bing double of a knot being a slice link: for n>1 the (n+1)-st iterated Bing double of a knot is rationally slice if and only if the n-th iterated Bing double of the knot is rationally slice. The main technique of the proof is a covering link construction simplifying a given link. We prove certain similar geometric obstructions for n <= 1 as well. Our results are sharp enough to conclude, when combined with algebraic invariants, that if the n-th iterated Bing double of a knot is slice for some n, then the knot is algebraically slice. Also our geometric arguments applied to the smooth case show that the Ozsvath-Szabo and Manolescu-Owens invariants give obstructions to iterated Bing doubles being slice. These results generalize recent results of Harvey, Teichner, Cimasoni, Cha and Cha-Livingston-Ruberman. As another application, we give explicit examples of algebraically slice knots with non-slice iterated Bing doubles by considering von Neumann rho-invariants and rational knot concordance. Refined versions of such examples are given, that take into account the Cochran-Orr-Teichner filtration. | |
| dc.description | 21 pages, 18 figures; typos fixed, sections 6 and 7 revised; to appear in Geometry and Topology | |
| dc.identifier | https://arxiv.org/abs/0712.3762 | |
| dc.identifier | http://arxiv.org/abs/0712.3762 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163816 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25, 57N70 | |
| dc.title | Covering link calculus and iterated Bing doubles | |
| dc.type | text |