Second-countable étale groupoids with polynomial growth are topologically amenable, and under compactness, metrizability, ampleness and minimality they satisfy weak m-comparison and Matui's AH conjecture.
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Amenability and comparison for \'etale groupoids with polynomial growth
Second-countable étale groupoids with polynomial growth are topologically amenable, and under compactness, metrizability, ampleness and minimality they satisfy weak m-comparison and Matui's AH conjecture.