A characterization of pseudo-Anosov foliations
type: Item
instance of: scholarly article
title: A characterization of pseudo-Anosov foliations
zbMATH Open document ID: 0602.57019
author: Athanase Papadopoulos
author: Robert Penner
published in: Pacific Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Let M be a closed oriented smooth surface of genus at least two. We address the problem of recognizing when an equivalence class of measured foliations on M is left invariant by some pseudo-Anosov map of M. Our solution to this problem is essentially combinatorial. Using train tracks, we associate a semi-infinite word in a finite alphabet to a class of measured foliations. Roughly, it is proved that a measured foliation class is invariant under a pseudo-Anosov map if and only if it admits an eventually periodic combinatorial word. The proof is in some sense constructive, and an algorithm for generating all conjugacy classes of pseudo-Anosov maps is described.
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 57N05
Mathematics Subject Classification ID: 57R50
zbMATH DE Number: 3971785
zbMATH Keywords: closed oriented smooth surface
zbMATH Keywords: measured foliations
zbMATH Keywords: pseudo-Anosov map
zbMATH Keywords: train tracks
MaRDI profile type: Publication
full work available at URL: pjm.1987.130.359
OpenAlex ID: W2076422355
DOI: 10.2140/PJM.1987.130.359
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description: scientific article; zbMATH DE number 3971785