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What is deRham Cohomology of S^n about?

The document summarizes the computation of the deRham cohomology of the n-sphere S^n. It proceeds by induction on n. For 1 < k < n, any closed k-form on S^n is exact by using a partition of unity argument on the union of two subsets homeomorphic to R^n. For k = 1, closed 1-forms are exact by integrating a potential function. For k = n, any n-form with integral 0 is exact. Therefore, H^k(S^n) is R for k = 0, n and 0 otherwise.

Author

Ricardo E.

Language

EN