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

Swarup Bhowmik; Deblina Das

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arXiv · 2606.29017

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

Swarup Bhowmik·Deblina Das

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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.

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BibTeX RIS

Swarup Bhowmik, Deblina Das. 2026-06-27. A structure theorem for centralizers of dilations in $QI(\mathbb{R}_{+})$. https://arxiv.org/abs/2606.29017

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