Work

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

Year: 2025

Type: article

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.

Source: Selecta Mathematica

DOI: 10.1007/s00029-025-01093-y

Authors: Thomas O. Rot, Lauran Toussaint

Institution: Vrije Universiteit Amsterdam

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Nederlandse Organisatie voor Wetenschappelijk Onderzoek