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Sur deux questions connexes de connexité concernant les feuilletages et leurs holonomies

Abstract : The two connectedness questions we are interested in refer to : – the space of codimension 1 foliations on a 3-manifold; – the space of representations of Z^2 into the group of smooth diffeomorphisms of the interval. The main result, which is proved in the second part of the dissertation, is the following : if two codimension 1 foliations on a closed 3-manifold have homotopic tangent subbundles, they can be linked by a continuous path of foliations. This statement hides a subtlety : if the given foliations are smooth, the path we construct can contain near its bounderies foliations which are only C^1. This is because we don't know whether the space of representations of Z^2 into the diffeomorphisms of the interval is connected or not. In an attempt to answer this very question, we pointed out the following phenomenon which is discussed in the first part of the dissertation : many smooth diffeomorphisms of R+ fixing only the origin have a C^infinite centralizer which is uncountable and dense in their C^1 centralizer (which is itself a one-parameter group). We also study the arithmetic properties of this subgroup.
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Contributor : Hélène Eynard-Bontemps Connect in order to contact the contributor
Submitted on : Thursday, November 26, 2009 - 12:02:36 PM
Last modification on : Tuesday, November 19, 2019 - 12:09:34 PM
Long-term archiving on: : Tuesday, October 16, 2012 - 2:55:44 PM

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Hélène Eynard-Bontemps. Sur deux questions connexes de connexité concernant les feuilletages et leurs holonomies. Mathématiques [math]. Ecole normale supérieure de lyon - ENS LYON, 2009. Français. ⟨tel-00436304⟩

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