Indian Journal of Pure and Applied Mathematics

, Volume 50, Issue 4, pp 877–881 | Cite as

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

  • Prateep ChakrabortyEmail author


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.

Key words

PL-homeomorphisms quasi-isometry center of group 


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The author thanks Aniruddha C. Naolekar, Parameswaran Sankaran, Ajay Singh Thakur and the anonymous referee for their valuable suggestions and comments.


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© Indian National Science Academy 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology KharagpurKharagpurIndia

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