Simple spheres in simply-connected 4-manifolds

2025/09/06 by Anthony Conway, Conway, Anthony
Mathematics · Computer Science · #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2509.05862

Abstract

These notes, which are based on three lectures delivered at the summer school "Topological 4-manifolds" at CRM in 2025, discuss classifications of locally flat spheres in closed, simply-connected 4-manifolds, with a focus on the case where the complements of the spheres have abelian fundamental group.

Citations

• Concordance of spheres in 4-manifolds with an immersed dual sphere
• Invariants of 2-knots
• Smoothly knotted and topologically unknotted nullhomologous surfaces in 4-manifolds
• Surfaces in 4-manifolds: Concordance, Isotopy, and Surgery

Related

• Will we ever classify simply-connected smooth 4-manifolds?
• Simple groups and complements of smooth surfaces in simply connected 4-manifolds
• 4-manifolds with boundary and fundamental group ℤ
• Six Lectures on Four 4-Manifolds
• Geography of spin symplectic 4-manifolds with abelian fundamental group