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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2002 • Question 5

Question

Math 6510 • Differentiable Manifolds Fall 2002 • Question 5

Using methods of differential topology prove that for each compact orientable differentiable manifold (without boundary) \(M\) of dimension \(m\), \(H^m(M,\mathbb {R})\ne 0\), where \(H^m(M,\mathbb {R})\) is the de Rham cohomology group.

Raw LaTeX

Using methods of differential topology prove that for each compact orientable
differentiable manifold (without boundary) \(M\) of dimension \(m\),
\(H^m(M,\mathbb{R})\ne0\), where \(H^m(M,\mathbb{R})\) is the de Rham cohomology group.

Topic Tags

Cohomology and Cup Products Homology with Coefficients Orientability and Volume Forms de Rham Cohomology