Geodesic
Theories of bundles with additional structures
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 8, pp. 77-98.

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In the present paper, we study bundles equipped with extra homotopy conditions, in particular, so-called $n$-bundles. It is shown that (under some condition) the classifying space of 1-bundles is the double coset space of some finite-dimensional Lie group. 
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A. V. Ershov. Theories of bundles with additional structures. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 8, pp. 77-98. http://geodesic.mathdoc.fr/item/FPM_2007_13_8_a5/

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