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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6520 • Algebraic Topology

Fall 2022 • Question 3

Question

Math 6520 • Algebraic Topology Fall 2022 • Question 3

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 the homology groups of \(\mathbb {R}P^n\) with coefficients in \(\mathbb {Z}/2\).

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 the homology groups of \(\mathbb{R}P^n\) with coefficients in \(\mathbb{Z}/2\).

Topic Tags

CW Complexes and Cell Attachments Cellular Homology Homology with Coefficients Real Projective Spaces