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Math · Advanced Math
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If n>1, show that the fundamental group of the n-fold torus is not abelian. [Hint: Let G be the free group on the set {αι, B1, . . . ,An, Br.); let F be the free group on the set {y, δ} . Consider the homomorphism of G onto F that sends αι and β1 to γ and all other αί and βί to δ.]

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