Covering link calculus and iterated Bing doubles
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- Title
- Covering link calculus and iterated Bing doubles
- Authors
- Cha, JC; Kim, T
- Date Issued
- 2008-01
- Publisher
- GEOMETRY & TOPOLOGY PUBLICATIONS
- Abstract
- 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 nonslice 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.
- Keywords
- KNOT CONCORDANCE GROUP; BOUNDARY LINKS; INVARIANTS; COBORDISM; HOMOLOGY
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/29419
- DOI
- 10.2140/GT.2008.12.2173
- ISSN
- 1364-0380
- Article Type
- Article
- Citation
- GEOMETRY & TOPOLOGY, vol. 12, page. 2173 - 2201, 2008-01
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