A combinatorial representation of curves using train tracks
type: Item
instance of: scholarly article
title: A combinatorial representation of curves using train tracks
zbMATH Open document ID: 0959.57016
DOI: 10.1016/S0166-8641(99)00077-2
author: Itaru Takarajima
published in: Topology and its Applications
publication date: 2001-02-22T00:00:00Z
review text: The author studies curves that are quasi-transversal to a given train track on a closed surface \(M\) of genus \(g\geq 2\). He shows that every homotopy class of a curve on \(M\) is represented by a quasi-transversal curve and that this representation is unique after a normalization. As an application he gives combinatorial algorithms to decide whether a given homotopy class can be represented by a simple closed curve and whether a given mapping class is periodic, pseudo-Anosov, or reducible.
reviewed by: Wolfgang Heil
Mathematics Subject Classification ID: 57N05
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 1507101
zbMATH Keywords: mapping class
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1507101