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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Free lines for homeomorphisms of the open annulus


Author: Lucien Guillou
Journal: Trans. Amer. Math. Soc. 360 (2008), 2191-2204
MSC (2000): Primary 37E30
Published electronically: November 28, 2007
MathSciNet review: 2366979
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Abstract: Let $ H $ be a homeomorphism of the open annulus $ S^1 \times {\bf R}$ isotopic to the identity and let $ h$ be a lift of $ H$ to the universal cover $ {\bf R} \times {\bf R}$ without fixed point. Then we show that $ h$ admits a Brouwer line which is a lift of a properly imbedded line joining one end to the other in the annulus or $ H$ admits a free essential simple closed curve.


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Additional Information

Lucien Guillou
Affiliation: Institut Fourier B.P. 74, Université Grenoble 1, Saint-Martin-d’Hères 38402 cedex France
Email: lguillou@ujf-grenoble.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04374-7
PII: S 0002-9947(07)04374-7
Keywords: Brouwer homeomorphism, free line, fixed point, open annulus, torus, Poincar\'e-Birkhoff Theorem
Received by editor(s): June 14, 2006
Published electronically: November 28, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.