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arXiv · 2307.08020

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

Thomas O. Rot·Lauran Toussaint
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Abstract

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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BibTeXRIS

Thomas O. Rot, Lauran Toussaint. 2023-07-16. Non-linear proper Fredholm maps and the stable homotopy groups of spheres. https://arxiv.org/abs/2307.08020

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