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
Full content URL: https://doi.org/10.1007/s10711-023-00790-2
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PMLA_ASOT_YSR_ThompsonRinfty_Final.pdf - Whole Document Available under License Creative Commons Attribution 4.0 International. 563kB |
| Item Type: | Article |
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| Item Status: | Live Archive |
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-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 |
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| 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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