Casson towers and slice links

• 成果类型: Article
• 署名作者: Cha, Jae Choon; Powell, Mark
• 署名单位: Pohang University of Science & Technology (POSTECH); Korea Institute for Advanced Study (KIAS); University of Quebec; University of Quebec Montreal
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0639-z
• 发表日期: 2016
• 页码: 413-457
• 关键词: knot concordance; fibered knots; filtration; cobordism; TOPOLOGY; surgery

摘要

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.