Hopf Invariant (Differential Topology)
Hello everyone, this is a problem out of Milnor (Topology from a Differentiable viewpoint) I have been assigned to solve. First, definition of the "Linking number"
Still with me? Ok, you can define the "Hopf Invariant" in the following way:
So I need to show three things (and any help on ANY them is appreciated :-) )
a) The Hopf Invariant is locally constant as a function of y.
b) If y and z and regular for g also and then
c) Prove depends only on the homotopy class of f and does not depend on the choice of y and z.
Basically, prove H(f) is a well-defined invariant. Any thoughts?