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arXiv · 2106.01527

A counterexample to the HK-conjecture that is principal

Robin J. Deeley
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Abstract

Scarparo has constructed counterexamples to Matui's HK-conjecture. These counterexample and other known counterexamples are essentially principal but not principal. In the present paper, a counterexample to the HK-conjecture that is principal is given. Like Scarparo's original counterexample, our counterexample is the transformation groupoid associated to a particular odometer. However, the relevant group is the fundamental group of a flat manifold (and hence is torsion-free) and the associated odometer action is free. The examples discussed here do satisfy the rational version of the HK-conjecture.

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Robin J. Deeley. 2022-02-24. A counterexample to the HK-conjecture that is principal. https://arxiv.org/abs/2106.01527

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