Jae Choon Cha
Casson towers and slice links
Cha, Jae Choon; Powell, Mark
Authors
Mark Powell
Abstract
We prove that a Casson tower of height 4 contains a flat embedded disc bounded by the attaching circle, and we prove disc embedding results for height 2 and 3 Casson towers which are embedded into a 4-manifold, with some additional fundamental group assumptions. In the proofs we create a capped grope from a Casson tower and use a refined height raising argument to establish the existence of a symmetric grope which has two layers of caps, data which is sufficient for a topological disc to exist, with the desired boundary. As applications, we present new slice knots and links by giving direct applications of the disc embedding theorem to produce slice discs, without first constructing a complementary 4-manifold. In particular we construct a family of slice knots which are potential counterexamples to the homotopy ribbon slice conjecture.
Citation
Cha, J. C., & Powell, M. (2016). Casson towers and slice links. Inventiones Mathematicae, 205(2), 413-457. https://doi.org/10.1007/s00222-015-0639-z
Journal Article Type | Article |
---|---|
Acceptance Date | Nov 24, 2015 |
Online Publication Date | Dec 9, 2015 |
Publication Date | Aug 1, 2016 |
Deposit Date | Oct 3, 2017 |
Publicly Available Date | Mar 28, 2024 |
Journal | Inventiones Mathematicae |
Print ISSN | 0020-9910 |
Electronic ISSN | 1432-1297 |
Publisher | Springer |
Peer Reviewed | Peer Reviewed |
Volume | 205 |
Issue | 2 |
Pages | 413-457 |
DOI | https://doi.org/10.1007/s00222-015-0639-z |
Related Public URLs | https://arxiv.org/abs/1411.1621 |
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Copyright Statement
The final publication is available at Springer via https://doi.org/10.1007/s00222-015-0639-z.
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