Homotopy classification of maps into homogeneous spaces

Sergiy Koshkin

We give an alternative to Postnikov's homotopy classification ofmaps 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 suitablefor extending the notion of homotopy to Sobolev maps. This is required in applicationsto variational problems of mathematical physics.

Journal of Homotopy and Related Structures, Vol. 4(2009), No. 1, pp. 331-346