Abstract
In this study, we introduce the notion of PLδ-homeomorphisms of Rn. 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(Rn), which comprises all quasi-isometries of Rn, is indeed trivial.
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