Title: On the Measure Equivalence of Baumslag-Solitar Groups and T(r,s) Tree Automorphism Groups

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• Damien Gaboriau (CNRS (Centre national de la recherche scientifique))
• Wednesday 09 July 2025, 11:45-12:45
• Seminar Room 1, Newton Institute.

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NPCW06 - Non-positive curvature and applications

In 2001, K. Whyte demonstrated that all Baumslag-Solitar groups BS(r,s), with |r|,|s|≠1 and |r|≠|s|, are quasi-isometric, thus completing the quasi-isometric classification of Baumslag-Solitar groups initiated by B. Farb and L. Mosher. Since then, the question of their measure equivalence has remained an open and intriguing problem. With A. Poulin, A. Tserunyan, R. Tucker-Drob, and K. Wrobel, we have solved this problem, thus establishing the counterpart of Whyte’s theorem in terms of measured equivalence. To do this we are led to a detour through the world of non-unimodular groups and actions which preserve only a class of measure (type III ) and we reduce the question to a problem of the theory of measured graphs in this framework.

This talk is part of the Isaac Newton Institute Seminar Series series.

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