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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2009 • Question 5

Question

Math 6510 • Differentiable Manifolds Spring 2009 • Question 5

Show that \(S^3\) (the 3-sphere) is the covering space of a manifold \(M\) which is not diffeomorphic to \(\mathbb {R}\mathrm {P}^3\). (Hint: find an appropriate finite group action on \(S^3\).)

Raw LaTeX

Show that \(S^3\) (the 3-sphere) is the covering space of a manifold \(M\)
which is not diffeomorphic to \(\RP^3\). (Hint: find an appropriate finite group
action on \(S^3\).)

Topic Tags

Covering Spaces Homotopy and Degree on Manifolds Lie Group Actions and Homomorphisms Real Projective Spaces