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.
Keywords
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