2022/10/18 by Marco Marengon, Marengon, Marco, Stefan Mihajlović +1
Computer Science · Mathematics · #57R10 #57R40 #57R42 #57R45 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Primary: 57K10. Secondary: 57K40
paper · pdf · doi:10.48550/arxiv.2210.10089
openalex publication_date 2022/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that all knots with unknotting number at most 21 are smoothly slice in the K3 surface. We also prove a more general statement for 4-manifolds that contain a plumbing tree of spheres. Our strategy is based on a flexible method to remove double points of immersed surfaces in 4-manifolds by tubing over neighbourhoods of embedded trees. As a byproduct, we recover a classical result of Norman and Suzuki that every knot is smoothly slice in S2 × S2 and in \mathbbCP2 # \mathbbCP2.