Opuscula Math. 41, no. 5 (2021), 667-683
https://doi.org/10.7494/OpMath.2021.41.5.667

 
Opuscula Mathematica

Coboundaries of commuting Borel automorphisms

Shrey Sanadhya

Abstract. We show that if \(S\), \(T\) are two commuting automorphisms of a standard Borel space such that they generate a free Borel \(\mathbb{Z}^2\)-action then \(S\) and \(T\) do not have same sets of real valued bounded coboundaries. We also prove a weaker form of Rokhlin Lemma for Borel \(\mathbb{Z}^d\)-actions.

Keywords: coboundries, Rokhlin Lemma, Borel \(\mathbb{Z}^d\)-action.

Mathematics Subject Classification: 37A40, 37A99, 37B99.

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  • Shrey Sanadhya
  • The University of Iowa, Department of Mathematics, 14 MacLean Hall, Iowa City, Iowa 52242, USA
  • Communicated by P.A. Cojuhari.
  • Received: 2021-05-29.
  • Revised: 2021-07-22.
  • Accepted: 2021-08-04.
  • Published online: 2021-09-30.
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Cite this article as:
Shrey Sanadhya, Coboundaries of commuting Borel automorphisms, Opuscula Math. 41, no. 5 (2021), 667-683, https://doi.org/10.7494/OpMath.2021.41.5.667

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