Otopy classification of gradient compact perturbations of identity in Hilbert space

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.

14 pages, 2 figures, minor changes, correction of typos