- Thread starter
- #1
Let $\gamma_0,\gamma_1$ and $\delta_0,\delta_1$ be four closed curves in U, all of which have the same initial point $z_0$ (for some parameterizations). Assume that $\gamma_0$ and $\delta_0$ are homotopic in U with homotophy given by $\Gamma_0$; and assume that $\gamma_1$ and $\delta_1$ are homotopic in U with homotophy given by $\Gamma_1$. Prove that the product curves $\gamma_0\gamma_1$ and $\delta_0\delta_1$ are also homotopic in U by exhibiting an explicit homotophy in terms of $\Gamma_0$ and $\Gamma_1$ (and showing briefly why it is a homotophy).
I am pretty lost on this problem.
I am pretty lost on this problem.