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Propriétés locales de l'espace des homéomorphismes de Brouwer

Published online by Cambridge University Press:  01 December 1999

MARC BONINO
MARC BONINO
Affiliation:
Université Paris 13, Institut Galilée, Dépt de Mathématiques, Avenue JB Clément, 93430 Villetaneuse, France (e-mail: bonino@zeus.math.univ-paris13.fr)
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Abstract

We consider in this paper the space of all orientation preserving and fixed point free homeomorphisms of the plane, endowed with the compact-open topology. Our main theorem asserts that this space is locally contractible. Then we give a new proof of the path connectedness. Finally, it is shown that the inclusion of this space into the space of all orientation preserving planar homeomorphisms induces the trivial map on the fundamental groups.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 6 , December 1999 , pp. 1405 - 1423
Copyright
1999 Cambridge University Press

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