Amenable L-2-Theoretic Methods and Knot Concordance
SCIE
SCOPUS
- Title
- Amenable L-2-Theoretic Methods and Knot Concordance
- Authors
- Cha, JC
- Date Issued
- 2014-01
- Publisher
- OXFORD UNIV PRESS
- Abstract
- We reveal new structures in the topological knot concordance group. As a key ingredient, we develop obstructions using L-2-theoretic methods for amenable groups in Strebel's class recently introduced by Orr and the author. Concerning (h)-solvable knots, which are defined in terms of certain Whitney towers of height h in bounding 4-manifolds, we show the following: for any n>1, there are (n)-solvable but non-(n. 5)-solvable (and therefore nonslice) knots, which are not detected by prior methods using Cochran-Orr-Teichner L-2-signature obstructions as well as Levine algebraic obstructions and Casson-Gordon invariants.
- Keywords
- BOUNDARY LINKS; BING DOUBLES; INVARIANTS; COBORDISM; HOMOLOGY; L-2-SIGNATURES; FILTRATION; HIRZEBRUCH; SIGNATURES; SERIES
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/13864
- DOI
- 10.1093/IMRN/RNT092
- ISSN
- 1073-7928
- Article Type
- Article
- Citation
- INTERNATIONAL MATHEMATICS RESEARCH NOTICES, vol. 2014, no. 17, page. 4768 - 4803, 2014-01
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