Successful collaboration of algebraists in Lincoln, Brazil and Germany results in a new paper accepted by “Geometriae Dedicata”

The paper Thompson-like groups, Reidemeister numbers, and fixed points by Paula M Lins de Araujo (University of Lincoln), Altair S. de Oliveira-Tosti (Northern Paraná State University) and Yuri Santos Rego (Otto von Guericke University Magdeburg) has been accepted for publication in Geometriae Dedicata.

Abstract: We investigate fixed-point properties of automorphisms of groups similar to R. Thompson’s group F. Revisiting work of Gonçalves-Kochloukova, we deduce a cohomological criterion to detect infinite fixed-point sets in the abelianization, implying the so-called property R∞. Using the BNS Σ-invariant and drawing from works of Gonçalves-Sankaran-Strebel and Zaremsky, we show that our tool applies to many F-like groups, including Stein’s F_2,3, Cleary’s F_τ’, the Lodha-Moore groups, and the braided version of F.