Hyperbolic structures on wreath products
Hyperbolic structures on wreath products
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花环产品上的双曲结构
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
S. Balasubramanya
中科院分区：
文献类型：
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作者：
S. Balasubramanya
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 {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 {mathbb{Z}_{n}mathbin{mathrm{wr}}mathbb{Z}} all have finitely many quasi-parabolic structures.
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 {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 {mathbb{Z}_{n}mathbin{mathrm{wr}}mathbb{Z}} all have finitely many quasi-parabolic structures.