Higher Dimensional Thompson Groups

By Matthew G. Brin. 2004

175 citations recorded by the source corpus.

We construct a "higher dimensional" version 2V of Thompson's group V. Like V it is an infinite, finitely presented, simple subgroup of the homeomorphism group of the Cantor set, but we show that it is not isomorphic to V by showing that the actions on the Cantor set are not topologically conjugate: 2V has an element with "chaotic" action, while V cannot have such an element. A theorem of Rubin is then applied which shows that for these two groups, isomorphism would imply topological conjugacy.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fd75aec343c0d3158d4b1ae463af2f793a0e0b2a

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The algebra of strand splitting. I. A braided version of Thompson's group V (2004, background): “It is generated by involutions [ 2, Section 12 ] and, if the metric on C is ignored, V can be viewed somewhat as a “Coxeter group” of permutations of C. In [4] we find presentations for BV and V that differ only in that the presentation for V has relations of the form x2 = 1 that are not present in ”
Etale groupoids arising from products of shifts of finite type (2015, background): “In [5, 6], he proved that Vk,r and 2V2,1 are not isomorphic, 2V2,1 is simple and 2V2,1 is finitely presented.”
Leavitt path algebras: the first decade (2014, background): “Then one verifies that the explicit isomorphism from Mr(LC(1, n)) to Ms(LC(1, n)) provided in the proof of Theorem 3.10 takes G+n,r onto G + n,s. ✷ For any three positive integers t, n, r (with n ≥ 2), Brin [51] constructed a group (denoted tVn,r) which can be viewed as a t-dimensional analog of the”