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Groups of PL-homeomorphisms admitting nontrivial invariant characters

Lima Gonçalves, Daciberg ; Sankaran, Parameswaran ; Strebel, Ralph

In: Pacific Journal of Mathematics, 2017, vol. 287, no. 1, p. 101–158

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...