Algebraic invariants of solenoid dynamics

A (weak) solenoid, also called solenoidal manifold, is the inverse limit of a system of covering maps between closed manifolds. To these spaces, we can associate a Cantor action, which can be regarded as a dynamical model. The main difficulty when using this approach is that this model is not unique: it is only well-defined up to return equivalence. We will introduce new algebraic invariants of Cantor actions that are invariant by return equivalences, and thus can be used to classify solenoids up to homeomorphism.