In this seminar we review the notion of Markov partitions for generalized pseudo-Anosov homeomorphisms (\gpA) and show how, through the associated incidence matrix, one can construct a subshift of finite type (SFT) that is semiconjugate to the corresponding pseudo-Anosov homeomorphism.

We then introduce geometric Markov partitions and the notion of geometric type, a combinatorial object that extends the information contained in the incidence matrix. We discuss how this geometric type allows for a refined combinatorial analysis of the associated SFT, leading to our main result: two \gp-Anosov homeomorphisms admit geometric partitions of the same geometric type if and only if they are topologically conjugate via an orientation-preserving homeomorphism.