Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2007 • Question 13

Question

Math 6510 • Differentiable Manifolds Fall 2007 • Question 13

Prove or disprove:

  1. For every \(d\in \mathbb {Z}\) there is a degree \(d\) map \(f_d:T^2\to S^2\).
  2. For every \(d\in \mathbb {Z}\) there is a degree \(d\) map \(g_d:S^2\to T^2\).

Raw LaTeX

Prove or disprove:
\begin{enumerate}
\item[a)] For every \(d\in\Z\) there is a degree \(d\) map
\(f_d:T^2\to S^2\).
\item[b)] For every \(d\in\Z\) there is a degree \(d\) map
\(g_d:S^2\to T^2\).
\end{enumerate}

Topic Tags

Degree Theory Homotopy and Degree on Manifolds