Homotopy classification of maps into homogeneous spaces

Mathematics – Geometric Topology

Scientific paper

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Appendix deleted, exposition improved, contact information updated; 13 pages, no figures

Scientific paper

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.

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