Non-displaceable contact embeddings and infinitely many leaf-wise intersections. (English) Zbl 1239.53106

Albers, Peter; McLean, Mark

J. Symplectic Geom. 9, No. 3, 271-284 (2011).

Summary: Using Lefschetz fibrations, we construct a large family of contact manifolds with the following properties: Any bounding contact embedding into an exact symplectic manifold satisfying a mild topological assumption is non-displaceable and generically has infinitely many leafwise intersection points. Moreover, any Stein filling of dimension at least six has infinite-dimensional symplectic homology.

MSC:

53D35	Global theory of symplectic and contact manifolds
57R17	Symplectic and contact topology in high or arbitrary dimension
53D10	Contact manifolds (general theory)

Keywords:

Lefschetz fibrations; bounding contact embedding; non-displaceable; Stein filling; symplectic homology