Simple groups and complements of smooth surfaces in simply connected 4‐manifolds
Abstract
Abstract For each integer we construct an oriented closed simply connected 4‐manifold admitting a smoothly embedded closed connected surface of self‐intersection number such that the complement of the surface has non‐trivial fundamental group. This answers a question of Kronheimer in Kirby's 1997 problem list. The proof combines a topological construction with homological properties of simple groups such as Thompson's group and certain sporadic finite simple groups.
Fields of Study & Subjects
Geometric and Algebraic Topology
Geometric Analysis and Curvature Flows
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Journal of Topology
- Volume
- 19
- Issue
- 3
- Publication date
- 1 September 2026
- Language
- EN