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- W2980355874 abstract "Abstract The study of the poset of hyperbolic structures on a group G was initiated by C. Abbott, S. Balasubramanya and D. Osin, [Hyperbolic structures on groups, Algebr. Geom. Topol. 19 2019, 4, 1747–1835, 10.2140/agt.2019.19.1747]. However, this poset is still very far from being understood, and several questions remain unanswered. In this paper, we give a complete description of the poset of hyperbolic structures on the lamplighter groups <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>wr</m:mi> <m:mo></m:mo> <m:msub> <m:mi>ℤ</m:mi> <m:mi>n</m:mi> </m:msub> <m:mi>ℤ</m:mi> </m:mrow> </m:math> {mathbb{Z}_{n}mathbin{mathrm{wr}}mathbb{Z}} and obtain some partial results about more general wreath products. As a consequence of this result, we answer two open questions regarding quasi-parabolic structures: we give an example of a group G with an uncountable chain of quasi-parabolic structures and prove that the lamplighter groups <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>wr</m:mi> <m:mo></m:mo> <m:msub> <m:mi>ℤ</m:mi> <m:mi>n</m:mi> </m:msub> <m:mi>ℤ</m:mi> </m:mrow> </m:math> {mathbb{Z}_{n}mathbin{mathrm{wr}}mathbb{Z}} all have finitely many quasi-parabolic structures." @default.
- W2980355874 created "2019-10-25" @default.
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- W2980355874 date "2019-10-15" @default.
- W2980355874 modified "2023-10-04" @default.
- W2980355874 title "Hyperbolic structures on wreath products" @default.
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- W2980355874 doi "https://doi.org/10.1515/jgth-2018-0176" @default.
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