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math.OA2026
Compact Quantum Metric Spaces from Weakly Geodesic Length Functions on Hyperbolic Groups
Are Austad
We show that length functions on hyperbolic groups whose induced metrics are hyperbolic and weakly geodesic naturally give rise to compact quantum metric spaces, thus generalizing…
math.DS2026
Amenability and comparison for étale groupoids with polynomial growth
Are Austad, Christian Bönicke
We show that any second-countable locally compact Hausdorff étale groupoid with polynomial growth is topologically amenable. If moreover the groupoid is compactly generated with co…
math.OA2026
Quantum metrics from length functions on étale groupoids
Are Austad
We show how to construct a compact quantum metric space from a proper continuous length function on an étale groupoid with compact unit space, where the unit space additionally has…