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On the contact mapping class group of Legendrian circle bundles

Part of: Symplectic geometry, contact geometry Differential topology Low-dimensional topology

Published online by Cambridge University Press:  01 February 2017

Emmanuel Giroux  and
Patrick Massot
Emmanuel Giroux
Affiliation:
Unité de Mathématiques Pures et Appliquées, École Normale Supérieure de Lyon, CNRS, 46 allée d’Italie, 69364 Lyon Cedex 07, France email [email protected]
Patrick Massot
Affiliation:
CMLS, École polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau Cedex, France email [email protected]
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Abstract

In this paper, we determine the group of contact transformations modulo contact isotopies for Legendrian circle bundles over closed surfaces of non-positive Euler characteristic. These results extend and correct those presented by the first author in a former work. The main ingredient we use is connectedness of certain spaces of embeddings of surfaces into contact 3-manifolds. This connectedness question is also studied for itself with a number of (hopefully instructive) examples.

Keywords

contact structuresmapping class groups

MSC classification

Primary: 57M50: Geometric structures on low-dimensional manifolds 57R17: Symplectic and contact topology
Secondary: 53D35: Global theory of symplectic and contact manifolds 53D10: Contact manifolds, general
Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 2 , February 2017 , pp. 294 - 312
Copyright
© The Authors 2017 

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