Factors of Toeplitz flows and other almost 1-1 extensions over group rotations

Abstract

If a minimal topological flow admits a symbolic extension then it also admits a symbolic almost 1-1 extension. The factors of symbolic almost automorphic flows are characterized as those almost automorphic flows which admit a symbolic extension. As an application, we provide concrete examples of factors of Toeplitz flows, which are neither Toeplitz flows nor odometers.