On homeomorphisms and quasi-isometries of the real line

Sankaran, Parameswaran

doi:10.1090/S0002-9939-05-08348-6

On homeomorphisms and quasi-isometries of the real line
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by Parameswaran Sankaran PDF

Proc. Amer. Math. Soc. 134 (2006), 1875-1880 Request permission

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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