On the contact mapping class group of Legendrian circle bundles

Emmanuel Giroux; Patrick Massot

doi:10.1112/s0010437x16007776

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arXiv · 1506.01162

On the contact mapping class group of Legendrian circle bundles

Emmanuel Giroux·Patrick Massot

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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 nonpositive 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. In the third section, this connectedness question is studied in more details with a number of (hopefully instructive) examples.

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Emmanuel Giroux, Patrick Massot. 2015-06-03. On the contact mapping class group of Legendrian circle bundles. https://doi.org/10.1112/s0010437x16007776

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