Thurston equivalence of topological polynomials

DOI10.1007/s11511-006-0007-3zbMath1176.37020arXivmath/0510082OpenAlexW1973067142MaRDI QIDQ858557

Laurent Bartholdi, Volodymyr V. Nekrashevych

Publication date: 10 January 2007

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0510082

zbMATH Keywords

branched coveringDehn twistrational mapsrabbit polynomialramification graphThurston's criterion

Mathematics Subject Classification ID

Geometric group theory (20F65) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Teichmüller theory for Riemann surfaces (30F60) Low-dimensional topology of special (e.g., branched) coverings (57M12) Combinatorics and topology in relation with holomorphic dynamical systems (37F20)

Related Items (37)

Mapping schemes realizable by obstructed topological polynomials ⋮ Self-similar groups, automatic sequences, and unitriangular representations ⋮ The Pullback Map on Teichmüller Space Induced from a Thurston Map ⋮ A minimal Cantor set in the space of 3-generated groups. ⋮ Dynamics of polynomial diffeomorphisms of \(\mathbb {C}^2\): combinatorial and topological aspects ⋮ Groups and semigroups defined by colorings of synchronizing automata ⋮ Exponential growth of some iterated monodromy groups ⋮ Algorithmic aspects of branched coverings. II/V: Sphere bisets and decidability of Thurston equivalence ⋮ Invariant spanning trees for quadratic rational maps ⋮ Hyperbolic groupoids and duality ⋮ On the simplicity of Nekrashevych algebras of contracting self-similar groups ⋮ Origami, affine maps, and complex dynamics ⋮ Mating, paper folding, and an endomorphism of ℙℂ² ⋮ Twisted matings and equipotential gluings ⋮ An algebraic formulation of Thurston's characterization of rational functions ⋮ Introduction to iterated monodromy groups ⋮ Algorithmic aspects of branched coverings ⋮ Teichmüller theory and critically finite endomorphisms ⋮ FINITE SELF-SIMILAR p-GROUPS WITH ABELIAN FIRST LEVEL STABILIZERS ⋮ Modular groups, Hurwitz classes and dynamic portraits of NET maps ⋮ Geometry and Algebra of the Deltoid Map ⋮ Iterated monodromy groups of quadratic polynomials. I. ⋮ AN UNCOUNTABLE FAMILY OF 3-GENERATED GROUPS WITH ISOMORPHIC PROFINITE COMPLETIONS ⋮ Pullback invariants of Thurston maps ⋮ Rationality is decidable for nearly Euclidean Thurston maps ⋮ C*-algebras and self-similar groups ⋮ Thurston's algorithm and rational maps from quadratic polynomial matings ⋮ Quadratic Thurston maps with few postcritical points ⋮ A group of non-uniform exponential growth locally isomorphic to $IMG(z^2+i)$ ⋮ Algorithmic aspects of branched coverings. III/V: Erasing maps, orbispaces, and the Birman exact sequence ⋮ Boundary values of the Thurston pullback map ⋮ Fixed-point-free elements of iterated monodromy groups ⋮ Book Review: Early days in complex dynamics: a history of complex dynamics in one variable during 1906–1942 ⋮ On the classification of critically fixed rational maps ⋮ The W. Thurston algorithm applied to real polynomial maps ⋮ Recognizing topological polynomials by lifting trees ⋮ SOLENOIDAL MAPS, AUTOMATIC SEQUENCES, VAN DER PUT SERIES, AND MEALY AUTOMATA

Cites Work

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• Surfaces and planar discontinuous groups. Revised and expanded transl. from the German by J. Stillwell
• A proof of Thurston's topological characterization of rational functions
• The Classification of Critically Preperiodic Polynomials as Dynamical Systems
• An algebraic formulation of Thurston’s combinatorial equivalence
• The Thurston equivalence for postcritically finite branched coverings

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