A prove that a closed k-form w on sk is exact if and only
(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.
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a prove that a closed k-form w on sk is exact if and only if intsk w 0 hint dim hksk 1b conclude that the linear map
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