Some remarks on topological full groups of Cantor minimal systems II

By H. Matui. Ergodic Theory and Dynamical Systems, 2004

123 citations recorded by the source corpus.

Abstract We prove that commutator subgroups of topological full groups arising from minimal subshifts have exponential growth. We also prove that the measurable full group associated to the countable, measure-preserving, ergodic and hyperfinite equivalence relation is topologically generated by two elements.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6cf3127f78a72690958e16b6c06c2483e2fdfb57

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Citations in the corpus

Palindromic subshifts and simple periodic groups of intermediate growth (2016, background): “ of all homeomorphisms h : X −→ X such that for every ζ ∈ X there exists a neighborhood U of ζ and an element g ∈ G such that h|U = g|U. Topological full groups were introduced in [4]. See the papers [10, 12, 13, 11] for various properties of topological full groups of group actions and ´etale group”
Groups acting on trees with almost prescribed local action (2015, background): “as recently received much attention. For example it has been proved that the derived subgroup of the topological full group associated to a minimal subshift, which is a ﬁnitely generated simple group [Mat06], is amenable [JM13] (see also [MB14]). Here we prove that the family of groups G(F,F′) provi”
Milnor's Problem on the Growth of Groups and its Consequences (2011, unknown): “Observe that [[T ]]′ always has exponential growth, as was recently shown in [169].”
Simple groups of dynamical origin (2015, background): “oores example [14], groups associated with expanding maps [20], diagram groups [7], etc. 1 2 V. NEKRASHEVYCH Topological full groups of ´etale groupoids were studied by H. Matui in a series of papers [15, 16, 17]. In particular, he showed that for some classes of groupoids the derived subgroup of th”
Cantor systems, piecewise translations and simple amenable groups (2012, background): “phic such groups. (Non-isomorphism follows from the Giordano–Putnam–Skau result since uncountably many minimal subshifts can be distinguished by their entropy; see the comments after Corollary 5.5 in [Mat06] for references.) In order to prove Theorem A, we reformulate the problem in terms of the gro”
Etale groupoids arising from products of shifts of finite type (2015, background): “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.”