Expansion complexes for finite subdivision rules. I

DOI10.1090/S1088-4173-06-00126-3zbMath1092.52502MaRDI QIDQ5477268

William J. Floyd, James W. Cannon, Walter R. Parry

Publication date: 30 June 2006

Published in: Conformal Geometry and Dynamics of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

conformal structures

Mathematics Subject Classification ID

Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Hyperbolic groups and nonpositively curved groups (20F67) Circle packings and discrete conformal geometry (52C26)

Related Items

Subdivision rules and virtual endomorphisms, Classification of subdivision rules for geometric groups of low dimension, Constructing rational maps from subdivision rules, Invariant Peano curves of expanding Thurston maps, Conformal tilings I: foundations, theory, and practice, Finite type coarse expanding conformal dynamics, Squaring rectangles for dumbbells, Lattès maps and finite subdivision rules, Expansion properties for finite subdivision rules. I., Constructing subdivision rules from rational maps, Conformal tilings II: Local isomorphism, hierarchy, and conformal type, Shape convergence for aggregate tiles in conformal tilings, Quasisymmetric uniformization and heat kernel estimates, Expansion complexes for finite subdivision rules. II

Cites Work

• A proof of Thurston's topological characterization of rational functions
• The combinatorial Riemann mapping theorem
• Geometry of cubulated 3-manifolds
• Expansion complexes for finite subdivision rules. II
• The Boundary of Negatively Curved Groups
• Homotopy Hyperbolic 3-Manifolds are Virtually Hyperbolic
• A “regular” pentagonal tiling of the plane
• Recognizing constant curvature discrete groups in dimension 3
• Finite subdivision rules
• Constructing rational maps from subdivision rules
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