2
votes
1answer
131 views

Construction of a classifying map from a connection 1-form

From a connection 1-form on $M$, I can construct a parallel transport from which in turn I can construct a classifying map $M \to BG$. Is there a construction of such a classifying map directly from a ...
11
votes
3answers
453 views

Can a homotopy inverse of the map from a Lie group to loops on its classifying space be given by holonomy?

Let $G$ be the compact Lie group $SO(n)$. There are some classical constructions of the classifying bundle of $G$ based upon on direct limits of Grassmann and Stiefel manifolds: $$BG \simeq ...