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Casson towers and slice links

Cha, Jae Choon; Powell, Mark

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Authors

Jae Choon Cha

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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