%0 Journal Article %T Theories of bundles with additional homotopy conditions %A A. V. Ershov %J Mathematics %D 2008 %I arXiv %X 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. %U http://arxiv.org/abs/0804.1119v3