Reeb foliations on S^5 and contact 5-manifolds violating the Thurston-Bennequin inequality

Details Reeb foliations on S^5 and contact 5-manifolds violating the Thurston-Bennequin inequality Reeb foliations on S^5 and contact 5-manifolds violating the Thurston-Bennequin inequality

2009-06-17

arxiv.org/abs/0906.3237v2

Mathematics

Geometric Topology

26 pages, 4 figures; this is the Feb 2010 version first submitted to a journal which contains new figures and new contents esp

Scientific paper

We obtain the following two results through foliation theoretic approaches including a review of Lawson's construction of a codimension-one foliation on the 5-sphere: 1) The standard contact structure on the 5-sphere deforms to `Reeb foliations'. 2) We define a 5-dimensional Lutz tube which contains a plastikstufe. Inserting it into any contact 5-manifold, we obtain a contact structure which violates the Thurston-Bennequin inequality for a convex hypersurface with contact-type boundary.

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