Otopy classification of gradient compact perturbations of identity in Hilbert space

TL;DR

This paper establishes a bijection between the otopy classes of gradient local maps and all local maps in Hilbert space, focusing on compact perturbations of the identity.

Contribution

It proves that the inclusion of gradient local maps into all local maps induces a bijection between their otopy classes in Hilbert space.

Findings

Bijection between otopy classes of gradient and all local maps.

Focus on compact perturbations of the identity.

Results applicable to Hilbert space maps.

Abstract

We prove that the inclusion of the space of gradient local maps into the space of all local maps from Hilbert space to itself induces a bijection between the sets of the respective otopy classes of these maps, where by a local map we mean a compact perturbation of identity with a compact preimage of zero.