Theories of bundles with additional homotopy conditions

TL;DR

This paper investigates bundles with extra homotopy conditions, focusing on simplicial n-bundles, their classifying spaces, and connections to C*-algebras, revealing new structural insights.

Contribution

It introduces the concept of simplicial n-bundles, characterizes their classifying spaces as double coset spaces, and explores their relation to C*-algebras.

Findings

Classifying space of 1-bundles as double coset space of a Lie group

Relation established between simplicial n-bundles and C*-algebras

Conditions under which the classifying space description holds

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.