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A group with Property (T) acting on the circle

Abstract : We exhibit a topological group G with property (T) acting non-elementarily and continuously on the circle. This group is an uncountable totally disconnected closed subgroup of Homeo + (S 1). It has a large unitary dual since it separates points. It comes from homeomorphisms of dendrites and a kaleidoscopic construction. Alternatively, it can be seen as the group of elements preserving some specific geodesic lamination of the hyperbolic disk. We also prove that this action is unique up to conjugation and that it can't be smoothened in any way. Finally, we determine the universal minimal flow of the group G.
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https://hal.archives-ouvertes.fr/hal-03029466
Contributor : Bruno Duchesne Connect in order to contact the contributor
Submitted on : Saturday, November 28, 2020 - 2:53:21 PM
Last modification on : Wednesday, November 3, 2021 - 7:56:42 AM

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  • HAL Id : hal-03029466, version 1

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Bruno Duchesne. A group with Property (T) acting on the circle. 2020. ⟨hal-03029466⟩

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