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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2014 • Question 8

Question

Math 6510 • Differentiable Manifolds Fall 2014 • Question 8

Describe a cell structure on the real projective space \(\mathbb {R}P^n\). Explicitly describe the attaching maps of all cells. Use this cell structure to compute \(H_i(\mathbb {R}P^n;\mathbb {Z}/2)\) for \(i\ge 0\).

Raw LaTeX

Describe a cell structure on the real projective space \(\mathbb{R}P^n\).
Explicitly describe the attaching maps of all cells. Use this cell structure to
compute \(H_i(\mathbb{R}P^n;\Z/2)\) for \(i\ge0\).

Topic Tags

CW Complexes and Cell Attachments Homology with Coefficients Real Projective Spaces