Almost 1-1 extensions of Furstenberg-Weiss type and test for amenability

María Isabel Cortez; Jaime Gomez

doi:10.1090/tran/9648

February 18, 2026Transactions of the American Mathematical Society

Almost 1-1 extensions of Furstenberg-Weiss type and test for amenability

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Key Points

The research aims to establish the existence of a minimal almost 1-1 extension of a Cantor system related to infinite residually finite groups.
Investigated minimal equicontinuous Cantor systems with free orbits.
Developed analysis of minimal extensions and almost 1-1 extensions within a group context.
Constructed a Borel equivariant map inducing an affine bijection between invariant measures.
Confirmed the existence of a minimal almost 1-1 extension of the Cantor system under the specified conditions.
Demonstrated the relationship between invariant probability measures of related spaces for both systems.

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Implication

This analysis demonstrates amenability in an infinite group using minimal equicontinuous systems, indicating new methods for examining group properties.

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Cortez et al. (2026) studied this question.

synapsesocial.com/papers/6997fa5aad1d9b11b3453728 https://doi.org/10.1090/tran/9648

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Almost 1-1 extensions of Furstenberg-Weiss type and test for amenability

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Almost 1-1 extensions of Furstenberg-Weiss type and test for amenability

Key Points

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Implication

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