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

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 dete...

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Bibliographic Details
Published in:arXiv.org 2023-07
Main Authors: Rot, Thomas O, Toussaint, Lauran
Format: Article
Language:English
Subjects:
Hilbert space
Online Access:Get full text
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Summary: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.
ISSN:2331-8422