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Talk: "Normal subgroups of the Lodha-Moore groups" (J. Burillo, UPC)

Abstract. The Lodha-Moore groups are nitely presented counterexamples to the von Neumann-Day conjecture, since they are not amenable but they do not contain free subgroups. They appear as subgroups of a group of piecewise projective maps constructed by Monod. I will introduce the group elements as maps and also as pairs of binary trees, in a similar way to Thompson's group F. We study their commutators and second commutators, showing some of them are simple. This leads to a complete description of the normal subgroups of these groups. This is joint work with Yash Lodha and with Lawrence Reeves.

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