A counterexample to the HK-conjecture that is principal

2021/06/03 by Robin J. Deeley, Deeley, Robin J. · 1 citation
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Geometric and Algebraic Topology #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2106.01527

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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• A Low-Dimensional Counterexample to the HK-Conjecture

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