On the contact mapping class group of Legendrian circle bundles

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 conn...

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Bibliographic Details
Published in:Compositio mathematica 2017-02, Vol.153 (2), p.294-312
Main Authors: Giroux, Emmanuel, Massot, Patrick
Format: Article
Language:English
Subjects:
Bundles
Conformal mapping
Contact
Eulers equations
Homomorphisms
Ingredients
Instructive
Isomorphism
Isotopes
Mapping
Mathematics
Neighborhoods
Subgroups
Topological manifolds
Toruses
Transformations (mathematics)
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Summary: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.
ISSN:0010-437X
1570-5846
DOI:10.1112/S0010437X16007776