An algebraic formulation of Thurston’s characterization of rational functions

Kevin M. Pilgrim[1]

  • [1] Dept. of Mathematics, Indiana University, Bloomington, IN, 47405 USA

Annales de la faculté des sciences de Toulouse Mathématiques (2012)

  • Volume: 21, Issue: S5, page 1033-1068
  • ISSN: 0240-2963

Abstract

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Following Douady-Hubbard and Bartholdi-Nekrashevych, we give an algebraic formulation of Thurston’s characterization of rational functions. The techniques developed are applied to the analysis of the dynamics on the set of free homotopy classes of simple closed curves induced by a rational function. The resulting finiteness results yield new information on the global dynamics of the pullback map on Teichmüller space used in the proof of the characterization theorem.

How to cite

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Pilgrim, Kevin M.. "An algebraic formulation of Thurston’s characterization of rational functions." Annales de la faculté des sciences de Toulouse Mathématiques 21.S5 (2012): 1033-1068. <http://eudml.org/doc/251019>.

@article{Pilgrim2012,
abstract = {Following Douady-Hubbard and Bartholdi-Nekrashevych, we give an algebraic formulation of Thurston’s characterization of rational functions. The techniques developed are applied to the analysis of the dynamics on the set of free homotopy classes of simple closed curves induced by a rational function. The resulting finiteness results yield new information on the global dynamics of the pullback map on Teichmüller space used in the proof of the characterization theorem.},
affiliation = {Dept. of Mathematics, Indiana University, Bloomington, IN, 47405 USA},
author = {Pilgrim, Kevin M.},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Thurston map; multicurve; obstruction; rational map; skinning map; mapping class group; virtual endomorphism},
language = {eng},
month = {12},
number = {S5},
pages = {1033-1068},
publisher = {Université Paul Sabatier, Toulouse},
title = {An algebraic formulation of Thurston’s characterization of rational functions},
url = {http://eudml.org/doc/251019},
volume = {21},
year = {2012},
}

TY - JOUR
AU - Pilgrim, Kevin M.
TI - An algebraic formulation of Thurston’s characterization of rational functions
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2012/12//
PB - Université Paul Sabatier, Toulouse
VL - 21
IS - S5
SP - 1033
EP - 1068
AB - Following Douady-Hubbard and Bartholdi-Nekrashevych, we give an algebraic formulation of Thurston’s characterization of rational functions. The techniques developed are applied to the analysis of the dynamics on the set of free homotopy classes of simple closed curves induced by a rational function. The resulting finiteness results yield new information on the global dynamics of the pullback map on Teichmüller space used in the proof of the characterization theorem.
LA - eng
KW - Thurston map; multicurve; obstruction; rational map; skinning map; mapping class group; virtual endomorphism
UR - http://eudml.org/doc/251019
ER -

References

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