Let $p_2:\mathbb S^1 \to \mathbb S^1$ be the two-sheeted covering map $p(z)=z^2$.If $f$ is odd($f(-z)=-f(z)$),show that there exists a continuous map $g:\mathbb S^1 \to \mathbb S^1$ such that $\deg f=\deg g$ and the following diagram commutes:$p_2 \circ f=g \circ p_2$
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
Here's how it works:
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top