On homeomorphisms and quasi-isometries of the real line期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On homeomorphisms and quasi-isometries of the real line

Authors:	Parameswaran Sankaran

Institution:	Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, India

Abstract:	We show that the group of piecewise-linear homeomorphisms of $\mathbb{R}$ having bounded slopes surjects onto the group $QI(\mathbb{R})$ of all quasi-isometries of $\mathbb{R}$ . We prove that the following groups can be imbedded in $QI(\mathbb{R})$ : the group of compactly supported piecewise-linear homeomorphisms of $\mathbb{R}$ , the Richard Thompson group , and the free group of continuous rank.

Keywords:	PL-homeomorphisms quasi-isometry Thompson's group free groups

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