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arXiv · 2212.03785

The uniform Gardner conjecture and rounding Borel flows

Matthew Bowen·Gábor Kun·Marcin Sabok
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Abstract

We study groups which satisfy Gardner's equidecomposition conjecture for uniformly distributed sets. We prove that an amenable group has this property if and only if it does not admit $(\mathbb{Z}/2\mathbb{Z}) *(\mathbb{Z}/2\mathbb{Z})$ as a quotient by a finite subgroup. Our technical contribution is an algorithm for rounding Borel flows for actions of amenable groups.

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BibTeXRIS

Matthew Bowen, Gábor Kun, Marcin Sabok. 2022-12-07. The uniform Gardner conjecture and rounding Borel flows. https://arxiv.org/abs/2212.03785

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