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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2009 • Question 12

Question

Math 6510 • Differentiable Manifolds Fall 2009 • Question 12

Is there a covering map \(p:X\to Y\) where

  1. \(X=S_3\), \(Y=S_2\) where \(S_g\) is a closed orientable surface of genus \(g\)?
  2. \(X\) is \(S_3\) with a small open disk removed and \(Y\) is \(S_2\) with a small open disk removed.

When \(p\) exists, what is the number of sheets?

Raw LaTeX

Is there a covering map \(p:X\to Y\) where
\begin{enumerate}
\item[(a)] \(X=S_3\), \(Y=S_2\) where \(S_g\) is a closed orientable surface of genus \(g\)?
\item[(b)] \(X\) is \(S_3\) with a small open disk removed and \(Y\) is \(S_2\) with a
small open disk removed.
\end{enumerate}
When \(p\) exists, what is the number of sheets?

Topic Tags

Covering Spaces Orientability and Volume Forms Smooth Manifolds and Embedded Submanifolds Surface Topology and Surface Groups