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