Casson towers and slice links

Cha, J. C. and Powell, M. (2016) Casson towers and slice links. Inventiones Mathematicae, 205(2), pp. 413-457. (doi: 10.1007/s00222-015-0639-z)

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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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Powell, Dr Mark
Authors: Cha, J. C., and Powell, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Inventiones Mathematicae
ISSN (Online):1432-1297
Published Online:09 December 2015
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