I do research mostly in general topology and topological dynamics, but I don't really see how AI would help, producing homeomorphic (topologically equivalent) spaces is not really the point.

In general even presenting a topological space to a computer is not easy. This can be done for very good spaces, for example those admitting (finite) triangulations, and there are some algorithms there, but my understanding is that you run into undecidability issues very quickly. But for the kind of spaces I work with (which are usually compact metrizable connected, so way better than arbitrary topological spaces) there seems to be no hope to get a computer to work with them.

Yes! I’m working on this in my PhD research. Here’s a relevant Caltech lecture aimed at a general scientific audience, discussing use of ML to detect equivalent knots.

https://m.youtube.com/watch?v=etNErJ1iuno