English

A counterexample to the HK-conjecture that is principal

K-Theory and Homology 2022-02-28 v2 Operator Algebras

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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Cite

@article{arxiv.2106.01527,
  title  = {A counterexample to the HK-conjecture that is principal},
  author = {Robin J. Deeley},
  journal= {arXiv preprint arXiv:2106.01527},
  year   = {2022}
}

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16 pages