Université de Fribourg

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...

Université de Fribourg

Infinite presentability of groups and condensation

Bieri, Robert ; Cornulier, Yves ; Guyot, Luc ; Strebel, Ralph

In: Journal of the Institute of Mathematics of Jussieu, 2014, vol. 13, no. 04, p. 811–848

We describe various classes of infinitely presented groups that are condensation points in the space of marked groups. A well-known class of such groups consists of finitely generated groups admitting an infinite minimal presentation. We introduce here a larger class of condensation groups, called infinitely independently presentable groups, and establish criteria which allow one to infer that a...

Université de Fribourg

Fitting quotients of finitely presented abelian-by-nilpotent groups

Groves, John Richard James ; Strebel, Ralph

In: Journal of Group Theory, 2014, vol. 17, no. 1, p. 1–12

We show that every finitely generated nilpotent group of class 2 occurs as the quotient of a finitely presented abelian-by-nilpotent group by its largest nilpotent normal subgroup.