Torsion in coinvariants of certain Cantor minimal Z^2-systems

TL;DR

This paper investigates the torsion properties of coinvariants in skew product extensions of Cantor minimal Z-systems, revealing torsion phenomena when the cocycle is non-degenerate and the group is non-cyclic.

Contribution

It demonstrates that non-cyclic G and non-degenerate cocycles induce torsion in the coinvariants of the skew product system.

Findings

Torsion appears in coinvariants for non-cyclic G with non-degenerate cocycles.

The result connects the algebraic properties of the group G with the topological dynamics.

Provides conditions under which torsion phenomena occur in these systems.

Abstract

Let G be a finite abelian group. We will consider a skew product extension of a product of two Cantor minimal Z-systems associated with a G-valued cocycle. When G is non-cyclic and the cocycle is non-degenerate, it will be shown that the skew product system has torsion in its coinvariants.