Geometriae Dedicata

, Volume 124, Issue 1, pp 153–190

A minimal Cantor set in the space of 3-generated groups

OriginalPaper

DOI: 10.1007/s10711-006-9118-4

Cite this article as:
Nekrashevych, V. Geom Dedicata (2007) 124: 153. doi:10.1007/s10711-006-9118-4

Abstract

We construct and study a family of 3-generated groups \(\mathcal{D}_w\) parametrized by infinite binary sequences w. We show that two groups of the family are isomorphic if and only if the sequences are cofinal and that two groups cannot be distinguished by finite sets of relations. We show a connection of the family with 2-dimensional holomorphic dynamics.

Keywords

Space of groupsSelf-Similar groupsIterated monodromy groups

Mathematics Subject Classification

20F65

Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA