In Chapter III we saw that, if X is any space with base point, then π n (X) = [S n , X] is a group for any positive integer n. In fact, n n is a functor from the category K 0 to the category of groups if n = 1, abelian groups if n > 1. In certain respects, they resemble the homology groups, and one of the objectives of this chapter is to pursue this analogy and see where it may lead.
KeywordsBase Point Fundamental Group Homology Group Homotopy Class Homotopy Group
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