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This is a Experimental Study study.

October 19, 2025Groups Geometry and DynamicsOpen Access

Measured groupoids beyond equivalence relations and group actions

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The study reveals genuine ergodic discrete measured groupoids not isomorphic to equivalence relations.
Key evidence includes a construction linked to B.H. Neumann's uncountable family of non-isomorphic groups.
An innovative construction method was applied to establish the distinctiveness of these groupoids.
The findings suggest a deeper understanding of groupoids and their applications in the study of symmetries and transformations.

Implication

This research uncovers ergodic discrete measured groupoids, indicating complexities beyond equivalence relations and transformation groupoids.

Abstract

We construct the first examples of genuine ergodic discrete measured groupoids that are not isomorphic to any equivalence relation or transformation groupoid. We use a construction due to B.H. Neumann of an uncountable family of pairwise non-isomorphic 2-generated groups for our result.

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Cite This Study

Soham Chakraborty (2025) studied this question.

synapsesocial.com/papers/68f43efb854d1061a58ac245 https://doi.org/10.4171/ggd/923

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Implication

This research uncovers ergodic discrete measured groupoids, indicating complexities beyond equivalence relations and transformation groupoids.

Measured groupoids beyond equivalence relations and group actions

Key Points

Implication

Abstract

Discussion

Cite This Study

Measured groupoids beyond equivalence relations and group actions

Key Points

Implication

Abstract

Discussion

Cite This Study

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