Non-linear proper Fredholm maps and the stable homotopy groups of spheres
Algebraic Topology
2023-07-18 v1 Functional Analysis
Geometric Topology
K-Theory and Homology
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.
Keywords
Cite
@article{arxiv.2307.08020,
title = {Non-linear proper Fredholm maps and the stable homotopy groups of spheres},
author = {Thomas O. Rot and Lauran Toussaint},
journal= {arXiv preprint arXiv:2307.08020},
year = {2023}
}
Comments
9 pages. Comments welcome