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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2005 • Question 11

Question

Math 6510 • Differentiable Manifolds Fall 2005 • Question 11

Carefully construct a \(\Delta \)-complex structure on \(\mathbb {R}P^2\) and use it to compute the homology groups of \(\mathbb {R}P^2\) with \(\mathbb {Z}\) and \(\mathbb {Z}_2\) coefficients.

Raw LaTeX

Carefully construct a \(\Delta\)-complex structure on \(\mathbb{R}P^2\) and use it to
compute the homology groups of \(\mathbb{R}P^2\) with \(\mathbb{Z}\) and \(\mathbb{Z}_2\)
coefficients.

Topic Tags

Cellular Homology Homology with Coefficients Real Projective Spaces Relative Homology and Long Exact Sequences