Mathematics Homework Solutions
#75958
Path-connected Space : Abelian Group
let x0 and x1 be points of the path-connected space X. Show that Pi_1(X,x0) is abelian iff for every pair a and b of paths from x0 to x1, we have a'=b', where a'([f])=[a-]*[f]*[a];( a- means the reverse of a.) and [f] belongs to Pi_1(X,x0). a':Pi_1(X,x0)->Pi_1(X,x1).
Path-connected Space and Abelian Groups are investigated. The solution is detailed and well presented.
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