A structure theorem for centralizers of dilations in $QI(\mathbb{R}_{+})$

Swarup Bhowmik; Deblina Das

A structure theorem for centralizers of dilations in $QI(\mathbb{R}_{+})$

Group Theory 2026-06-27 v1

Authors: Swarup Bhowmik , Deblina Das

Abstract

We study centralizers of dilations in the quasi-isometry group of the positive real line. We introduce an asymptotic invariant defined via coarsely dense sequences at infinity and establish a rigidity theorem for quasi-isometries that coarsely commute with a dilation. As an application, we identify the subgroup of the centralizer consisting of elements with non-empty asymptotic invariant and prove that it is naturally isomorphic to the multiplicative group of positive real numbers.

Cite

@article{arxiv.2606.29017,
  title  = {A structure theorem for centralizers of dilations in $QI(\mathbb{R}_{+})$},
  author = {Swarup Bhowmik and Deblina Das},
  journal= {arXiv preprint arXiv:2606.29017},
  year   = {2026}
}

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13 pages