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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2009 • Question 15

Question

Math 6510 • Differentiable Manifolds Fall 2009 • Question 15

Describe an explicit cell decomposition of \(\mathbb {C}P^n\) (including the precise subsets corresponding to cells; you don’t have to check all properties of cell structures). From the cell decomposition read off all homology and cohomology groups with \(\mathbb {Z}\) coefficients.

Raw LaTeX

Describe an explicit cell decomposition of \(\mathbb{C}P^n\) (including the
precise subsets corresponding to cells; you don't have to check all properties of
cell structures). From the cell decomposition read off all homology and cohomology
groups with \(\Z\) coefficients.

Topic Tags

Cellular Homology Cohomology and Cup Products Homology with Coefficients de Rham Cohomology