Suppose \(\phi:S^1\to S^1\) and \(\psi:S^1\to S^1\) are continuous maps. Show that the compositions \(\phi\circ\psi\) and \(\psi\circ\phi\) are homotopic.
Hint: Is this true for \(f(z)=z^n\), where \(n\in\mathbb Z\)?
Compositions of two self-maps of the circle are homotopic
P-TOP-WORKSHOP-QPH-03
- Area
- Topology
- Topics
- Degree, Homotopy
- Status
- draft