One stabilization is not enough for closed knotted surfaces

2023/04/04 by Kyle Hayden, Hayden, Kyle, Sungkyung Kang +3
Mathematics · #57R52 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2304.01504

openalex publication_date 2023/04/04 · openalex created_date 2023/04/07 · openalex updated_date 2026/08/01

Abstract

In this brief note, we show that there exist smooth 4-manifolds (with nonempty boundary) containing pairs of exotically knotted 2-spheres that remain exotic after one (either external or internal) stabilization. It follows that the ``one is enough'' theorem of Auckly-Kim-Melvin-Ruberman-Schwartz does not hold for closed surfaces whose homology classes are characteristic.

Related

• Smoothly knotted surfaces that remain distinct after many internal stabilizations
• One stabilization is not enough for contractible 4-manifolds
• For Exotic Surfaces with Boundary, One Stabilization is Not Enough
• An atomic approach to Wall-type stabilization problems
• Internal and external stabilization of exotic surfaces in 4-manifolds