On the center of the group of quasi-isometries of the real line

Prateep Chakraborty ()
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Prateep Chakraborty: Indian Institute of Technology Kharagpur

Indian Journal of Pure and Applied Mathematics, 2019, vol. 50, issue 4, 877-881

Abstract: Abstract Let QI(ℝ) denote the group of all quasi-isometries f : ℝ → ℝ. Let Q+(and Q−) denote the subgroup of QI(ℝ) consisting of elements which are identity near −∞ (resp. +∞). We denote by QI+(ℝ) the index 2 subgroup of QI(ℝ) that fixes the ends +∞, −∞. We show that QI+(ℝ) ≅ Q+ × Q−. Using this we show that the center of the group QI(ℝ) is trivial.

Keywords: PL-homeomorphisms; quasi-isometry; center of group (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13226-019-0360-5

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