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- W4360951736 abstract "Abstract We investigate fixed-point properties of automorphisms of groups similar to Richard Thompson’s group $$F$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>F</mml:mi> </mml:math> . 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 $$R_infty $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>∞</mml:mi> </mml:msub> </mml:math> . Using the Bieri–Neumann–Strebel $$varSigma $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>Σ</mml:mi> </mml:math> -invariant and drawing from works of Gonçalves–Sankaran–Strebel and Zaremsky, we show that our tool applies to many $$F$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>F</mml:mi> </mml:math> -like groups, including Stein’s group $$F_{2,3}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>F</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> </mml:math> , cleary’s irrational-slope group $$F_tau $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>τ</mml:mi> </mml:msub> </mml:math> , the Lodha–Moore groups, and the braided version of $$F$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>F</mml:mi> </mml:math> ." @default.
- W4360951736 created "2023-03-26" @default.
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- W4360951736 date "2023-03-25" @default.
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- W4360951736 title "Thompson-like groups, Reidemeister numbers, and fixed points" @default.
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- W4360951736 doi "https://doi.org/10.1007/s10711-023-00790-2" @default.
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