An algebraic formulation of Thurston's combinatorial equivalence

Author:
Kevin M. Pilgrim

Journal:
Proc. Amer. Math. Soc. **131** (2003), 3527-3534

MSC (2000):
Primary 37F20; Secondary 20F28, 20F36, 20E05

DOI:
https://doi.org/10.1090/S0002-9939-03-07035-7

Published electronically:
May 7, 2003

MathSciNet review:
1991765

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be an orientation-preserving branched covering for which the set of strict forward orbits of critical points is finite and let . To we associate an injective endomorphism of the free group , well-defined up to postcomposition with inner automorphisms. We show that two such maps are combinatorially equivalent (in the sense introduced by Thurston for the characterization of rational functions as dynamical systems) if and only if are conjugate by an element of which is induced by an orientation-preserving homeomorphism.

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Additional Information

**Kevin M. Pilgrim**

Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405-7106

Email:
pilgrim@indiana.edu

DOI:
https://doi.org/10.1090/S0002-9939-03-07035-7

Keywords:
Postcritically finite,
endomorphism of free group

Received by editor(s):
June 20, 2002

Published electronically:
May 7, 2003

Additional Notes:
This research was supported by Indiana University, Bloomington

Communicated by:
Michael Handel

Article copyright:
© Copyright 2003
American Mathematical Society