The strong topological Rokhlin property and Medvedev degrees of SFTs

TL;DR

This paper establishes a link between the Medvedev degrees of subshifts of finite type and the strong topological Rokhlin property in recursively presented groups, providing new insights and examples in the field.

Contribution

It simplifies the criterion for the absence of the strong topological Rokhlin property and introduces new examples of groups lacking this property.

Findings

Groups with nonzero Medvedev degree subshifts lack the strong topological Rokhlin property

The criterion for the property is simplified

New examples of groups without the property are provided

Abstract

We prove that if a recursively presented group admits a (nonempty) subshift of finite type with nonzero Medvedev degree then it fails to have the strong topological Rokhlin property. This result simplifies a known criterion and provides new examples of recursively presented groups without this property.