Finitely presented groups associated with expanding maps - Texas A&M University (TAMU) Scholar

We associate with every locally expanding self-covering $f:M o M$ of a compact path connected metric space a finitely presented group $V_f$. We prove that this group is a complete invariant of the dynamical system: two groups $V_{f_1}$ and $V_{f_2}$ are isomorphic as abstract groups if and only if the corresponding dynamical systems are topologically conjugate. We also show that the commutator subgroup of $V_f$ is simple, and give a topological interpretation of $V_f/V_f'$.

Finitely presented groups associated with expanding maps Academic Article