On Null-homology and stationary sequences

Gerold Alsmeyer, Chiranjib Mukherjee

Published 2019-10-16Version 1

The concept of homology, originally developed as a useful tool in algebraic topology, has by now become pervasive in quite different branches of mathematics. The notion particularly carries over quite naturally to the setup of measure-preserving transformations arising from various group actions or, equivalently, the setup of stationary sequences considered in this paper. Our main result provides a sharp criterion which determines (and rules out) when two stationary processes belong to the same {\it null-homology equivalence class}. We also discuss some concrete cases where the notion of null-homology turns up in a relevant manner.