degree (map of spheres)
Given a non-negative integer , let denote the -dimensional sphere. Suppose is a continuous map. Applying the reduced homology functor , we obtain a homomorphism . Since , it follows that is a homomorphism . Such a map must be multiplication by an integer . We define the degree of the map , to be this .
0.1 Basic Properties
If we identify , then the map defined by has degree . It is also possible, for any positive integer , and any integer , to construct a map of degree .
|Title||degree (map of spheres)|
|Date of creation||2013-03-22 13:22:12|
|Last modified on||2013-03-22 13:22:12|
|Last modified by||drini (3)|