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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1994 • Question 17

Question

Math 6510 • Differentiable Manifolds Fall 1994 • Question 17

Compute the deRham cohomology of \(S^2\) in four distinct ways. You may assume the singular cohomology groups \(H^*(S^2,\mathbb {R})\). Hint: one way could be from first principles using the Poincaré Lemma.

Raw LaTeX

Compute the deRham cohomology of \(S^2\) in four distinct ways. You
may assume the singular cohomology groups \(H^*(S^2,\mathbb{R})\). Hint: one way
could be from first principles using the Poincar\'e Lemma.

Topic Tags

Cohomology and Cup Products Homology with Coefficients de Rham Cohomology