Some remarks on the size of tubular neighborhoods in contact topology and fillability

Details Some remarks on the size of tubular neighborhoods in contact topology and fillability Some remarks on the size of tubular neighborhoods in contact topology and fillability

2008-12-11

arxiv.org/abs/0812.2108v2

Geometry & Topology 14 (2010) 719-754

Mathematics

Symplectic Geometry

19 pages, 2 figures; added example of manifold that is not fillable by neighborhood criterium; typos

Scientific paper

10.2140/gt.2010.14.719

The well-known tubular neighborhood theorem for contact submanifolds states that a small enough neighborhood of such a submanifold N is uniquely determined by the contact structure on N, and the conformal symplectic structure of the normal bundle. In particular, if the submanifold N has trivial normal bundle then its tubular neighborhood will be contactomorphic to a neighborhood of Nx{0} in the model space NxR^{2k}. In this article we make the observation that if (N,\xi_N) is a 3-dimensional overtwisted submanifold with trivial normal bundle in (M,\xi), and if its model neighborhood is sufficiently large, then (M,\xi) does not admit an exact symplectic filling.

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