Unknotting number 21 knots are slice in K3

Marengon, Marco and Mihajlović, S. (2025) Unknotting number 21 knots are slice in K3. MATHEMATICAL RESEARCH LETTERS, 32 (3). pp. 939-955. ISSN 1073-2780

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Abstract

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 CP2#CP2 © 2025 International Press, Inc.. All rights reserved.

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