Thompson-like groups, Reidemeister numbers, and fixed points

M. Lins de Araujo, Paula, S. de Oliveira-Tosti, Altair and Santos Rego, Yuri (2023) Thompson-like groups, Reidemeister numbers, and fixed points. Geometriae Dedicata, 217 (54). ISSN 0046-5755

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Thompson-like groups, Reidemeister numbers, and fixed points
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Item Type:Article
Item Status:Live Archive


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-infinity. Using the Bieri–Neumann–Strebel Sigma-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_τ , the Lodha–Moore groups, and the braided version of F.

Keywords:Thompson groups, Property R-infinity, Fixed points, BNS Sigma-invariant
Subjects:G Mathematical and Computer Sciences > G110 Pure Mathematics
Divisions:College of Science > School of Mathematics and Physics
ID Code:54130
Deposited On:18 Apr 2023 12:33

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