Geometriae Dedicata

, Volume 124, Issue 1, pp 153–190 | Cite as

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



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.


Space of groups Self-Similar groups Iterated monodromy groups 

Mathematics Subject Classification



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© Springer Science + Business Media B.V. 2007

Authors and Affiliations

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

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