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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2014 • Question 11

Question

Math 6510 • Differentiable Manifolds Spring 2014 • Question 11

Prove that there is no map \(h:\mathbb {R}\mathrm {P}^3\to \mathbb {R}\mathrm {P}^2\) that induces an isomorphism between fundamental groups. Hint: use cup products with \(\mathbb {Z}/2\mathbb {Z}\) coefficients. State all theorems you are using.

Raw LaTeX

Prove that there is no map \(h:\RP^3\to\RP^2\) that induces an isomorphism
between fundamental groups. Hint: use cup products with \(\Z/2\Z\) coefficients.
State all theorems you are using.

Topic Tags

Cohomology and Cup Products Fundamental Groups Pullbacks and Wedge Products Real Projective Spaces