The relative Whitney trick and its applications

• Christopher W. Davis ^[2] ; Patrick Orson ^[1] ; JungHwan Park ^[3]
  1. [1] Max Planck Institute for Mathematics

     Max Planck Institute for Mathematics

     Kreisfreie Stadt Bonn, Alemania

     
  2. [2] University of Wisconsin–Eau Claire, USA
  3. [3] KAIST, Corea del Sur

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 2, 2022
• Idioma: inglés
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• Resumen

  • We introduce a geometric operation, which we call the relative Whitney trick, that removes a single double point between properly immersed surfaces in a 4-manifold with boundary.Using the relative Whitney trick we prove that every link in a homology sphere is homotopic to a link that is topologically slice in a contractible topological 4-manifold. We further prove that any link in a homology sphere is order k Whitney tower concordant to a link in S3 for all k. Finally, we explore the minimum Gordian distance from a link in S3 to a homotopically trivial link. Extending this notion to links in homology spheres, we use the relative Whitney trick to make explicit computations for 3-component links and establish bounds in general.