On homeomorphisms and quasi-isometries of the real line

Details On homeomorphisms and quasi-isometries of the real line On homeomorphisms and quasi-isometries of the real line

2006-06-16

arxiv.org/abs/math/0606385v1

Proc. Amer. Math. Soc. 134 (2006), no. 7, (1875-1889)(electronic)

Mathematics

Geometric Topology

9 pages

Scientific paper

We show that the group of all pl-homeomorphisms of the reals having bounded
slopes surjects on the group $QI({\Bbb R})$ of all quasi-isometries of ${\Bbb
R}$. We prove that the following groups can be imbedded in $QI({\Bbb R})$: The
group of compactly supported pl-homeomorphisms of the reals, the Richard
Thompson group F, and the free group of rank the continuum.

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