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Chern character for torsion-free ample groupoids
[Submitted on 9 Sep 2025 (v1), last revised 12 Jun 2026 (this ve · 2026-06-15 · via math updates on arXiv.org

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Abstract:For an ample groupoid with torsion-free stabilizers, we construct a Chern character map going from the domain of the Baum-Connes assembly map of G to the Crainic-Moerdijk homology groups of G with rational coefficients. Assuming the (rational) Baum-Connes conjecture, this implies that the operator K-groups of the groupoid C*-algebra are rationally isomorphic to the periodicized groupoid homology groups, confirming a variation of Matui's HK conjecture. Our construction hinges on the recent $\infty$-categorical viewpoint on bivariant K-theory. We also present applications to the homology of hyperbolic dynamical systems, the homology of topological full groups, the homotopy type of the algebraic K-theory spectrum of ample groupoids, and the Elliott invariant of classifiable C*-algebras.

Submission history

From: Makoto Yamashita [view email]
[v1] Tue, 9 Sep 2025 12:31:27 UTC (63 KB)
[v2] Fri, 12 Jun 2026 09:07:23 UTC (59 KB)

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