I found this visualization regarding homotpy in wikipedia:
https://commons.wikimedia.org/wiki/File:Homotopy_curves.png
I would be very grateful if you could explai me all the abbreviations being used. I guess t stands for t and s for space, so that H (t,s) would be a homotopy in time t and space s. But what does gamma stand for, a given homotopy path? Would we call x and y the origo points of the homotopy?
Thanks in advance.
Have you read the Wikipedia page for homotopy already? That might be helpful.
In the picture you link, there are two paths with endpoints $x$ and $y$. The names of those paths happen to be $\gamma_0$ and $\gamma_1$. While $\gamma$ is a common variable for a path, I do not know where that convention comes from. The function $H$ is a homotopy between the two paths $\gamma_0$ and $\gamma_1$. The letter $H$ is chosen to stand for homotopy. The letter $t$ is a common parameter for the paths, and can sometimes be interpreted as "time". $s$ is a common companion variable to $t$, and it may help you to remember how path homotopies like $H(t,s)$ work if you think of it as "space", but I doubt that was why $s$ was chosen here.
Note: the intent is likely for $H(t,0)=\gamma_0(t)$ and $H(t,1)=\gamma_1(t)$ for all $t$.