Homotopy ribbon discs with a fixed group

Conway, Anthony¹

¹ Massachusetts Institute of Technology, Cambridge, MA, United States, Department of Mathematics, University of Texas at Austin, Austin, TX, United States

Algebraic and Geometric Topology, Tome 24 (2024) no. 8, pp. 4575-4587

Résumé

In the topological category, the classification of homotopy ribbon discs is known when the fundamental group G of the exterior is ℤ and the Baumslag–Solitar group BS ⁡ (1,2). We prove that if a group G is geometrically 2–dimensional and satisfies the Farrell–Jones conjecture, then a condition involving the fundamental group ensures that exteriors of aspherical homotopy ribbon discs with fundamental group G are s–cobordant rel boundary. When G is good, this leads to the classification of such discs. As an application, for any knot J ⊂ S3 whose knot group G(J) is good, we classify the homotopy ribbon discs for J # −J whose complement has group G(J). A similar application is obtained for BS ⁡ (m,n) when |m − n| = 1.

Détail

DOI : 10.2140/agt.2024.24.4575

Keywords: slice disk, homotopy ribbon disk, classification of ribbon disks, slice knot, surgery theory