Finitely generated simple left orderable groups, commutator width and orderable monsters

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• Yash Lodha (École polytechnique fédérale de Lausanne)
• Friday 10 May 2019, 13:45-14:45
• CMS, MR13.

If you have a question about this talk, please contact Richard Webb.

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In 1980 Rhemtulla asked whether there exist finitely generated simple left orderable groups.

In joint work with Hyde, we construct continuum many such examples (up to isomorphism), thereby resolving this question. In recent joint work with Hyde, Navas, and Rivas, we demonstrate that among these examples are also so called “left orderable monsters”. This means that all their actions on the real line are of a certain desirable dynamical type. This resolves Question 4 from Navas’s 2018 ICM proceedings article concerning the existence of such groups. In this talk I will provide a brief introduction to these groups and their striking structural properties.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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