English

Hyperbolic Structures on Wreath Products

Group Theory 2018-09-05 v1

Abstract

The study of the poset of hyperbolic structures on a group GG was initiated in a paper by C.Abbott, S.Balasubramanya and D.Osin. 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 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 with an uncountable chain of quasi-parabolic structures and prove that the Lamplighter groups all have finitely many quasi-parabolic structures.

Keywords

Cite

@article{arxiv.1809.00776,
  title  = {Hyperbolic Structures on Wreath Products},
  author = {Sahana H Balasubramanya},
  journal= {arXiv preprint arXiv:1809.00776},
  year   = {2018}
}
R2 v1 2026-06-23T03:53:14.044Z