Prove that a closed k-form w on s

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(a) Prove that a closed k-form w on S^k is exact if and only if int_(S^k) w = 0. [Hint: dim H^k(S^k) = 1.]
(b) Conclude that the linear map int_(S^k): H^k(S^k) -> R is an isomorphism.

Reference: Ex. 4.8.5 of Guillemin.

Reference no: EM13745264

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