Knotted surfaces with simply-connected complements

2026/07/16 by Audrick Pyronneau
Mathematics · #math.GT

paper · pdf

Abstract

We study locally flat, compact, oriented, genus g, surfaces with boundary a fixed knot K, properly embedded in simply-connected 4-manifolds with boundary the 3-sphere, and whose complements have trivial fundamental group. We show that if two such surfaces are homologous then they are topologically ambiently isotopic rel. boundary.

Related

• Unknotting Nonorientable Surfaces of Genus 4 and 5
• Locally flat simple spheres in ℂ P²
• Immersed surfaces with knot group ℤ
• Smoothly knotted and topologically unknotted nullhomologous surfaces in 4-manifolds
• Simple groups and complements of smooth surfaces in simply connected 4-manifolds