Topologically and rationally slice knots

• Jennifer Hom ^[1] ; Sungkyung Kang ^[2] ; JungHwan Park ^[3]
  1. [1] Georgia Institute of Technology

     Georgia Institute of Technology

     Estados Unidos

     
  2. [2] University of Oxford

     University of Oxford

     Oxford District, Reino Unido

     
  3. [3] Department of Mathematical Sciences, Korea Advanced Institute for Science and Technology, Daejeon, South Korea

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 2, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01020-1
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• Resumen

  • A knot in S3 is topologically slice if it bounds a locally flat disk in B4. A knot in S3 is rationally slice if it bounds a smooth disk in a rational homology ball. We prove that the smooth concordance group of topologically and rationally slice knots admits a Z∞ subgroup. All previously known examples of knots that are both topologically and rationally slice were of order two. As a direct consequence, it follows that there are infinitely many topologically slice knots that are strongly rationally slice but not slice.

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