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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2017 • Question 1

Question

Math 6510 • Differentiable Manifolds Fall 2017 • Question 1

Let \(\mathbf {P}^n(\mathbb {R})\) be \(n\)-dimensional real projective space. Use an explicit collection of charts to prove that \(\mathbf {P}^n(\mathbb {R})\) is a smooth manifold.

Raw LaTeX

Let \(\mathbf{P}^n(\R)\) be \(n\)-dimensional real projective space. Use an
explicit collection of charts to prove that \(\mathbf{P}^n(\R)\) is a smooth
manifold.

Topic Tags

Homotopy and Degree on Manifolds Real Projective Spaces Smooth Manifolds and Embedded Submanifolds Stokes' Theorem and Integration on Manifolds