Vol. 287, No. 1, 2017

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ISSN: 0030-8730
Groups of PL-homeomorphisms admitting nontrivial invariant characters

Daciberg Lima Gonçalves, Parameswaran Sankaran and Ralph Strebel

Vol. 287 (2017), No. 1, 101–158
Abstract

We show that several classes of groups G of PL-homeomorphisms of the real line admit nontrivial homomorphisms χ : G that are fixed by every automorphism of G. The classes enjoying the stated property include the generalizations of Thompson’s group F studied by K. S. Brown (1992), M. Stein (1992), S. Cleary (1995), and Bieri and Strebel (2016), but also the class of groups investigated by Bieri, Neumann, and Strebel (Theorem 8.1 in Invent. Math. 90 (1987), 451–477). It follows that every automorphism of a group in one of these classes has infinitely many associated twisted conjugacy classes.

Keywords
groups of PL-homeomorphisms of the real line, Bieri–Neumann–Strebel invariants, twisted conjugacy
Mathematical Subject Classification 2010
Primary: 20E45
Secondary: 20E36, 20F28
Milestones
Received: 12 December 2015
Revised: 28 June 2016
Accepted: 10 August 2016
Published: 6 February 2017
Authors
Daciberg Lima Gonçalves
Instituto de Matemática e Estatística da Universidade de São Paulo
Departamento de Matemática
Rua do Matão, 1010 CEP 05508-090
São Paulo-SP
Brazil
Parameswaran Sankaran
The Institute of Mathematical Sciences
CIT Campus
Chennai 600113
India
Ralph Strebel
Département de Mathématiques
Université de Fribourg
Chemin du Musée 23
CH-1700 Fribourg
Switzerland