English

Higher Dimensional Thompson Groups

Group Theory 2013-09-04 v1

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.

Keywords

Cite

@article{arxiv.math/0406046,
  title  = {Higher Dimensional Thompson Groups},
  author = {Matthew G. Brin},
  journal= {arXiv preprint arXiv:math/0406046},
  year   = {2013}
}

Comments

27 pages To appear in Geometriae Dedicata