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:
“Heaven has a Sea of Glass on which angels go sliding every afternoon. There are many golden streets, but the principal thoroughfares are Amen Street and Hallelujah Avenue, which intersect in front of the Throne. These streets play tunes when walked on, and all shoes have songs in them.”
—For the State of Florida, 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)