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Swarup Bhowmik

Publications and source records attributed to Swarup Bhowmik.

5 recordsLinked to original sources
arXiv2026

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

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.

math.GR↗
arXiv2025

Orderability and Asymptotic Structure of $\mathrm{QI}(\mathbb{R}^n)$

In this article, we study the algebraic and dynamical structure of certain normal subgroups of the quasi-isometry group of Euclidean spaces. We first consider the normal subgroup consisting of quasi-isometries that are asymptotically equal to the identity, and introduce a nested family of normal subgroups that distinguish different orders of sublinear deviation from the identity. We show that the centers of the resulting quotient groups are trivial. We further prove that these quotient groups are neither left-orderable nor locally indicable. We also introduce an asymptotic topology on the quasi-isometry group, yielding a natural metric structure on the quotient and providing a framework for studying large-scale invariants.

math.GT↗
arXiv2023

A Combinatorial Criterion and Center for the quasi-isometry groups of Euclidean spaces

In this study, we introduce the notion of $PL_δ$-homeomorphisms of $\mathbb{R}^n$. Furthermore, we provide a combinatorial criterion reliant on the vertices and edges of simplicial structures, to determine whether a piecewise-linear homeomorphism to be a quasi-isometry. By employing this criterion, we subsequently show that the center of the group $QI(\mathbb{R}^n)$, which comprises all quasi-isometries of $\mathbb{R}^n$, is indeed trivial.

math.GT↗
arXiv2023

A structure theorem and left-orderability of a quotient of quasi-isometry group of the real line

It is well-known that $QI(\mathbb{R})\cong(QI(\mathbb{R}_{+})\times QI(\mathbb{R}_{-}))\rtimes $, where $QI(\mathbb{R})$(resp. $QI(\mathbb{R}_{+})(\cong QI(\mathbb{R_-}))$) is the group of quasi-isometries of the real line (resp. $[0,\infty)$). We introduce an invariant for the elements of $QI(\mathbb{R_{+}})$ and split it into smaller units. We give an almost characterization of the elements of these units. We also show that a quotient of $QI(\mathbb{R_{+}})$ gives an example of a left-orderable group which is not locally indicable.

math.GT↗