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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
Posted:
December 19, 2005
MathSciNet review:
2215114
Full-text PDF Free Access
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Abstract: We show that the group of piecewise-linear homeomorphisms of  having bounded slopes surjects onto the group  of all quasi-isometries of  . We prove that the following groups can be imbedded in  : the group of compactly supported piecewise-linear homeomorphisms of  , the Richard Thompson group  , 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
Email:
sankaran@imsc.res.in
DOI:
http://dx.doi.org/10.1090/S0002-9939-05-08348-6
PII:
S 0002-9939(05)08348-6
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
Posted:
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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