Cantor systems, piecewise translations and simple amenable groups

By Kate Juschenko, Nicolas Monod. 2012

215 citations recorded by the source corpus.

We provide the rst examples of nitely generated simple groups that are amenable (and innite). To this end, we prove that topological full groups of minimal systems are amenable. This follows from a general existence result on invariant states for piecewise-translations of the integers. The states are obtained by constructing a suitable family of densities on the classical Bernoulli space.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/94b5c9626ea5c3d0dc09ed33db92c9a9816a5746

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In Atomic and Molecular Physics, and Optics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Etale groupoids arising from products of shifts of finite type (2015, background): “ ﬂip conjugacy. Later, in [26], it was shown that the commutator subgroup D([[G]]) is simple and that D([[G]]) is ﬁnitely generated if and only if the Z-action is expansive. K. Juschenko and N. Monod [20] proved that [[G]] is amenable. By these results, we obtained inﬁnitely many countable inﬁnite g”
Extensions of amenable groups by recurrent groupoids (2013, background): “The class of groups generated by homeomorphisms of bounded type includes some known examples of non-elementary amenable groups (groups of bounded automata [BKN10] and topological full group of minimal homeomorphisms of the Cantor set [JM12]), as well as groups whose amenability was an open question ”
LOCALLY NORMAL SUBGROUPS OF TOTALLY DISCONNECTED GROUPS. PART II: COMPACTLY GENERATED SIMPLE GROUPS (2014, background): “roup if and only if both con(g) and con(g−1) are compact. Thus an example for Question 3 would also be an example for [68, Problem 4.1]. By the recent groundbreaking work of K. Juschenko and N. Monod [32] and its extension due to V. Nekrashevych [43], there exist ﬁnitely generated inﬁnite simple ame”