Journal article

Groups of PL-homeomorphisms admitting nontrivial invariant characters

  • Lima Gonçalves, Daciberg Instituto de Matemática e Estatística da Universidade de São Paulo, Departamento de Matemática, São Paulo, Brazil
  • Sankaran, Parameswaran The Institute of Mathematical Sciences, CIT Campus, Chennai, India
  • Strebel, Ralph Département de Mathématiques, Université de Fribourg, Switzerland
Published in:
  • Pacific Journal of Mathematics. - 2017, vol. 287, no. 1, p. 101–158
English We show that several classes of groups G of PL-homeomorphisms of the real line admit nontrivial homomorphisms χ:G→R 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.
Faculté des sciences et de médecine
Département de Mathématiques
  • English
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