Abstract
We investigate fixed-point properties of automorphisms of groups similar to Richard Thompson’s group F. Revisiting work of Gonçalves and Kochloukova, we deduce a cohomological criterion to detect infinite fixed-point sets in the abelianization, implying the so-called property R_infty . Using the Bieri–Neumann–Strebel varSigma -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 group F_{2,3}, cleary’s irrational-slope group F_tau , the Lodha–Moore groups, and the braided version of F.
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