Casson towers and slice links

Cha, Jae Choon et Powell, Mark (2015). « Casson towers and slice links ». Inventiones mathematicae, pp. 1-45.

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Résumé

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.

Type:	Article de revue scientifique
Mots-clés ou Sujets:	Solitar Group, Seifert Surface, Whitehead Link, Fundamental Group Non-abelian Free Group, Hopf Link, Euler Number, Connected Sum, Dual Curve, Double Point, Free Product, Symplectic Basis, Proper Immersion Boundary Component, Line Bundle
Unité d'appartenance:	Faculté des sciences > Département de mathématiques
Déposé par:	Mark Powell
Date de dépôt:	27 avr. 2016 19:23
Dernière modification:	19 mai 2016 18:14
Adresse URL :	http://archipel.uqam.ca/id/eprint/8345

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