Non-linear proper Fredholm maps and the stable homotopy groups of spheres

• Thomas O. Rot ^[1] ; Lauran Toussaint ^[1]
  1. [1] VU University Amsterdam

     VU University Amsterdam

     Países Bajos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 5, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01093-y
• Enlaces
  • Texto completo
• Resumen

  • We classify non-linear proper Fredholm maps between Hilbert spaces, up to proper homotopy, in terms of the stable homotopy groups of spheres. We show that there is a surjective map from the stable homotopy groups of spheres to the set of non-linear proper Fredholm maps up to proper homotopy and determine the non-trivial kernel.

    We also discuss the case of oriented non-linear proper Fredholm maps which are in bijection with the stable homotopy groups of spheres.

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