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Higher Dimensional Thompson Groups

Matthew G. Brin
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Abstract

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.

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Matthew G. Brin. 2004-06-02. Higher Dimensional Thompson Groups. https://doi.org/10.1007/s10711-004-8122-9

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