What question did this study set out to answer?

This research aims to define a pairing between groupoid homology and invariant Borel probability measures, particularly for étale groupoids without totally disconnected base spaces.

August 8, 2026Proceedings of the Royal Society of Edinburgh Section A MathematicsOpen Access

A trace pairing and Elliott invariant for groupoid homology

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This research aims to define a pairing between groupoid homology and invariant Borel probability measures, particularly for étale groupoids without totally disconnected base spaces.
Defined a pairing between Crainic–Moerdijk groupoid homology and Borel measures.
Analyzed the implications for the Elliott invariant of C*-algebras.
Explored the relationship with K-theory.
The new pairing provides refined information over existing measures of clopen subsets.
For many groupoids, the new Elliott invariant aligns with existing C*-algebraic invariants.
Establishes a refinement of Matui’s HK conjecture for pertinent groupoids.

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Implication

Randomized trial investigates a pairing in groupoid homology, suggesting refined insights into C*-algebras.

Cite This Study

Deeley et al. (2026) studied this question.

synapsesocial.com/papers/6a76da9bf12abadc79815005 https://doi.org/10.1017/prm.2026.10170

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A trace pairing and Elliott invariant for groupoid homology

Key Points

Discussion

Implication

Cite This Study

A trace pairing and Elliott invariant for groupoid homology

Key Points

Discussion

Implication

Cite This Study

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