cotangent bundle is a bundle

Verifying the first criterion is simply a matter of writing it out:


This is obviously a homeomorphism.

As for the second criterion,

j=1ngαβji(x1,,x2n)ϕβj(x1,,x2n) = j=n2n(σαβ(x1,xn))ixjxj+n
= σαβi+n(x1,,x2n)
= ϕαi(x1,,x2n)

The third criterion follows from the chain rule:

Title cotangent bundle is a bundle
Canonical name CotangentBundleIsABundle
Date of creation 2013-03-22 14:54:31
Last modified on 2013-03-22 14:54:31
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 6
Author rspuzio (6075)
Entry type Proof
Classification msc 58A32