Topo-isomorphisms of irregular Toeplitz subshifts for residually finite groups
A talk in the Mathematik in den Naturwissenschaften series by
Jaime Gómez
| Abstract: | Let $G$ be a contable residually finite group. For each $\overleftarrow{G}$ totally disconnected metric compactification of $G$, there exists an irregular Toeplitz subshift contained in $\{0, 1\}^G$ such that it is a topo-isomorphic extension of $\overleftarrow{G}$. In this talk, we give a description of how this result is obtained. First, we need to establish sufficient conditions in order for a Toeplitz subshift to have invariant measures as
limit points of some sequence of periodic measures. After that, we will see some details on the definition of the irregular Toeplitz subshift, for instance, every possi-ble invariant measure of this subshift is a limit point of periodic measures. Finally, we guarantee that this Toeplitz subshift is a topo-isomorphic extension of $\overleftarrow{G}$. If we additionally assume that $G$ is amenable, we obtain new examples of mean-equicontinuous systems which are extensions of totally disconnected compactifica-tions of $G$. Within the CRC this talk is associated to the project(s): A6 |