Let M and N be differentiable manifolds. Let alpha: M -> N be a local diffeomorphism. Prove that if N is orientable, then M is orientable.© BrainMass Inc. brainmass.com October 24, 2018, 7:32 pm ad1c9bdddf
Differentiable Manifolds and Diffeomorphisms are investigated. The solution is detailed and well presented.
Inverse Function Theorem, Isomorphisms and Diffeomorphisms
Inverse Function Theorem. Let M and N be differentiable manifolds, φ : M -> N a differentiable mapping and p Є M such that dφp : TM ?> T(p)N is an isomorphism. Prove that is a local diffeomorphism at p; that is, there are neighborhoods U C M of p and V C N of p(p) such that φ : U ?> V is a diffeomorphism.