Homotopy classification of maps into homogeneous spaces

TL;DR

This paper presents a new homotopy classification method for maps into homogeneous spaces, facilitating the extension to Sobolev maps and aiding variational problems in physics.

Contribution

It offers an alternative to Postnikov's classification, describing homotopy classes via lifts to G, suitable for Sobolev maps and physical applications.

Findings

Provides a lift-based homotopy classification for maps into G/H.

Enables extension of homotopy notions to Sobolev maps.

Facilitates applications in variational problems of mathematical physics.

Abstract

We give an alternative to Postnikov's homotopy classification of maps from 3-dimensional CW-complexes to homogeneous spaces G/H of Lie groups. It describes homotopy classes in terms of lifts to the group G and is suitable for extending the notion of homotopy to Sobolev maps. This is required for applications to variational problems of mathematical physics.