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- W3205199710 abstract "Abstract A group 𝐺 is said to have property <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mi>R</m:mi> <m:mi mathvariant=normal>∞</m:mi> </m:msub> </m:math> R_{infty} if, for every automorphism <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>φ</m:mi> <m:mo>∈</m:mo> <m:mrow> <m:mi>Aut</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>G</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> varphiinmathrm{Aut}(G) , the cardinality of the set of 𝜑-twisted conjugacy classes is infinite. Many classes of groups are known to have this property. However, very few examples are known for which <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mi>R</m:mi> <m:mi mathvariant=normal>∞</m:mi> </m:msub> </m:math> R_{infty} is geometric , i.e., if 𝐺 has property <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mi>R</m:mi> <m:mi mathvariant=normal>∞</m:mi> </m:msub> </m:math> R_{infty} , then any group quasi-isometric to 𝐺 also has property <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mi>R</m:mi> <m:mi mathvariant=normal>∞</m:mi> </m:msub> </m:math> R_{infty} . In this paper, we give examples of groups and conditions under which <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mi>R</m:mi> <m:mi mathvariant=normal>∞</m:mi> </m:msub> </m:math> R_{infty} is preserved under commensurability. The main tool is to employ the Bieri–Neumann–Strebel invariant." @default.
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- W3205199710 date "2021-10-07" @default.
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- W3205199710 title "Twisted conjugacy and commensurability invariance" @default.
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- W3205199710 doi "https://doi.org/10.1515/jgth-2020-0130" @default.
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