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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Free lines for homeomorphisms of the open annulus
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by Lucien Guillou PDF
Trans. Amer. Math. Soc. 360 (2008), 2191-2204 Request permission

Abstract:

Let $H$ be a homeomorphism of the open annulus $S^1 \times \textbf {R}$ isotopic to the identity and let $h$ be a lift of $H$ to the universal cover $\textbf {R} \times \textbf {R}$ 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
  • Received by editor(s): June 14, 2006
  • Published electronically: November 28, 2007
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 2191-2204
  • MSC (2000): Primary 37E30
  • DOI: https://doi.org/10.1090/S0002-9947-07-04374-7
  • MathSciNet review: 2366979