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On homeomorphisms and quasi-isometries of the real line

Author: Parameswaran Sankaran
Journal: Proc. Amer. Math. Soc. 134 (2006), 1875-1880
MSC (2000): Primary 20F65, 20F28; Secondary 20F67
Published electronically: December 19, 2005
MathSciNet review: 2215114
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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 $ F$, and the free group of continuous rank.

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Additional Information

Parameswaran Sankaran
Affiliation: Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, India

Keywords: PL-homeomorphisms, quasi-isometry, Thompson's group, free groups
Received by editor(s): October 4, 2004
Received by editor(s) in revised form: February 8, 2005
Published electronically: December 19, 2005
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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