Classification of Principal Bundles
Any topological group G admits a classifying space BG: the quotient of some weakly contractible space EG, i.e. a topological space for which all its homotopy groups are trivial by a free action of G. The classifying space has the property that any G principal bundle over a paracompact manifold B is isomorphic to a pullback of the principal bundle . In fact, more is true, as the set of isomorphism classes of principal G bundles over the base B identifies with the set of homotopy classes of maps B → BG.
Read more about this topic: Principal Bundle
Famous quotes containing the words principal and/or bundles:
“The principal saloon was the Howlin’ Wilderness, an immense log cabin with a log fire always burning in the huge fireplace, where so many fights broke out that the common saying was, “We will have a man for breakfast tomorrow.””
—For the State of California, U.S. public relief program (1935-1943)
“He bundles every forkful in its place,
And tags and numbers it for future reference,
So he can find and easily dislodge it
In the unloading. Silas does that well.
He takes it out in bunches like birds’ nests.”
—Robert Frost (1874–1963)