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arXiv · 1207.4527

Topological isomorphism for rank-1 systems

Su Gao·Aaron Hill
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Abstract

We define the Polish space $\mathcal{R}$ of non-degenerate rank-1 systems. Each non-degenerate rank-1 system can be viewed as a measure-preserving transformation of an atomless, $σ$-finite measure space and as a homeomorphism of a Cantor space. We completely characterize when two non-degenerate rank-1 systems are topologically isomorphic. We also analyze the complexity of the topological isomorphism relation on $\mathcal{R}$, showing that it is $F_σ$ as a subset of $\mathcal{R} \times \mathcal{R}$ and bi-reducible to $E_0$. We also explicitly describe when a non-degenerate rank-1 system is topologically isomorphic to its inverse.

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Su Gao, Aaron Hill. 2013-03-13. Topological isomorphism for rank-1 systems. https://arxiv.org/abs/1207.4527

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