so we just covered markov chains in a probability course, not in the context of measure theory though, just basic discrete state space discrete time markov chains. im guessing the next step is to cover measure spaces if i wanna read more about markov chains, but im wondering at this point, if its interesting or possible to endow the state space with additional structure, like assuming group structure, or assuming the markov chain's state space forms a manifold. actually, i'd really like to know what to read next if i wanna study markov chains with manifold state space. id ask my proofs but i graduated a month ago! could anyone point out to me a good textbook on stochastic processes on manifold state space? would i need to know algebraic topology to cover that?