Theories of bundles with additional homotopy conditions

Abstract

In the present paper we study bundles equipped with extra homotopy conditions, in particular so-called simplicial $n$-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. We also establish some relation between our bundles and C*-algebras.

22 pages; v3: a new material in subsections 1.4. and 1.5. is added, minor changes and corrections