The plain sphere number of a link
Abstract
Let L be a link in S 3 .We consider a natural class of meridional presentations for π 1 (S 3 \ L) in which the relations are witnessed by certain embedded twospheres easily observed in a fixed diagram of L. The Wirtinger presentation is a special case.We prove that the bridge number of L equals the smallest number of generators of π 1 (S 3 \ L) over all such presentations.
Fields of Study & Subjects
Geometric and Algebraic Topology
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Publication details
- Journal / source
- Pacific Journal of Mathematics
- Volume
- 342
- Issue
- 2
- Pages
- 217–233
- Publication date
- 23 April 2026
- Language
- EN