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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2009 • Question 9

Question

Math 6510 • Differentiable Manifolds Spring 2009 • Question 9

Construct a \(\Delta \)-complex structure on \(\mathbb {R}\mathrm {P}^2\) and use it to calculate the homology and cohomology of of \(\mathbb {R}\mathrm {P}^2\) with \(\mathbb {Z}\) and \(\mathbb {Z}_2\) coefficients.

Raw LaTeX

Construct a \(\Delta\)-complex structure on \(\RP^2\) and use it to calculate
the homology and cohomology of of \(\RP^2\) with \(\Z\) and \(\Z_2\) coefficients.

Topic Tags

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