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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Summer 2016 • Question 10

Question

Math 6510 • Differentiable Manifolds Summer 2016 • Question 10

Describe a cell structure on real projective space \(\mathbb {R}\mathrm {P}^n\) and use it to compute all the cohomology groups \(H^i(\mathbb {R}\mathrm {P}^n,\mathbb {Z})\) and \(H^i(\mathbb {R}\mathrm {P}^n,\mathbb {Z}/2)\).

Raw LaTeX

Describe a cell structure on real projective space \(\RP^n\) and use it to
compute all the cohomology groups \(H^i(\RP^n,\Z)\) and \(H^i(\RP^n,\Z/2)\).

Topic Tags

Cohomology and Cup Products Homology with Coefficients Real Projective Spaces de Rham Cohomology