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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Classification of subdivision rules for geometric groups of low dimension
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by Brian Rushton
Conform. Geom. Dyn. 18 (2014), 171-191
Published electronically: October 7, 2014


Subdivision rules create sequences of nested cell structures on CW-complexes, and they frequently arise from groups. In this paper, we develop several tools for classifying subdivision rules. We give a criterion for a subdivision rule to represent a Gromov hyperbolic space, and show that a subdivision rule for a hyperbolic group determines the Gromov boundary. We give a criterion for a subdivision rule to represent a Euclidean space of dimension less than 4. We also show that Nil and Sol geometries cannot be modeled by subdivision rules. We use these tools and previous theorems to classify the geometry of subdivision rules for low-dimensional geometric groups by the combinatorial properties of their subdivision rules.
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Bibliographic Information
  • Brian Rushton
  • Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
  • Email:
  • Received by editor(s): April 7, 2014
  • Received by editor(s) in revised form: May 1, 2014, May 19, 2014, and June 22, 2014
  • Published electronically: October 7, 2014
  • © Copyright 2014 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 18 (2014), 171-191
  • MSC (2010): Primary 20F65, 05C25, 57M50
  • DOI:
  • MathSciNet review: 3266238