|
Free lines for homeomorphisms of the open annulus
Author(s):
Lucien
Guillou
Journal:
Trans. Amer. Math. Soc.
360
(2008),
2191-2204.
MSC (2000):
Primary 37E30
Posted:
November 28, 2007
MathSciNet review:
2366979
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
Let  be a homeomorphism of the open annulus  isotopic to the identity and let  be a lift of  to the universal cover  without fixed point. Then we show that  admits a Brouwer line which is a lift of a properly imbedded line joining one end to the other in the annulus or  admits a free essential simple closed curve.
References:
-
- 1.
- S. Addas-Zanata, Some extensions of the Poincaré-Birkhoff theorem to the cylinder and a remark on mappings of the torus homotopic to Dehn twists, Nonlinearity 18 (2005), 2243-2260. MR 2164740 (2006h:37064)
- 2.
- L.E.J. Brouwer, Beweis des ebenen Translationssatzes, Math. Ann., 72 (1912), 37-54. MR 1511684
- 3.
- F. Béguin, S. Crovisier, F. Le Roux, Pseudo-rotations of the open annulus, Bull. Braz. Math. Soc. 37 (2006), 275-306. MR 2266384
- 4.
- M. Bestvina, M. Handel, An area preserving homeomorphism of
 that is fixed point free but does not move any essential simple closed curve off itself, Ergod. Th. and Dynam. Sys., 12 (1992), 673-676. MR 1200335 (94d:58119) - 5.
- J. Franks, Generalizations of the Poincaré-Birkhoff theorem, Ann. of Math., 128 (1988), 139-151. MR 951509 (89m:54052)
- 6.
- L. Guillou, Théorème de translation plane de Brouwer et généralisations du théorème de Poincaré-Birkhoff, Topology, 33 (1994), 331-351. MR 1273787 (95h:55003)
- 7.
- B. de Kérékjartó, Vorlesüngen uber Topologie, Springer, Berlin (1923).
- 8.
- B. de Kérékjartó, The plane translation theorem of Brouwer and the last geometric theorem of Poincaré, Acta Sci. Math. Szeged, 4 (1928-29), 86-102.
- 9.
- P. Le Calvez, Une version feuilletée équivariante du théorème de translation de Brouwer, Publications IHES, 102 (2005), 1-98. MR 2217051
- 10.
- A. Sauzet, Application des décompositions libres à l'étude des homéomorphismes de surfaces, Ph.D. thesis, Université Paris-Nord (2001).
- 11.
- H. Terasaka, Ein Beweis des Brouwerschen ebenen Translationssatzes, Japan J. of Math., 7 (1930), 61-69.
- 12.
- H.E. Winkelnkemper, A generalisation of the Poincaré-Birkhoff theorem, Proc. AMS, 102 (1988), 1028-1030. MR 934887 (89e:55006)
- 13.
- G. Whyburn, E. Duda, Dynamic Topology, Springer Verlag, 1979. MR 526764 (80e:54001)
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (2000):
37E30
Retrieve articles in all Journals with
MSC (2000):
37E30
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:
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
Posted:
November 28, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
