Stein fillable 3manifolds admit positive open book decompositions along arbitrary links
Abstract
It is known by A. Loi and R. Piergallini that a closed, oriented, smooth 3manifold is Stein fillable if and only if it has a positive open book decomposition. In the present paper we will show that for every link L in a Stein fillable 3manifold there exists an additional knot L' to L such that the union of the links L and L' is the binding of a positive open book decomposition of the Stein fillable 3manifold. To prove the assertion, we will use the divide, which is a generalization of real morsification theory of complex plane curve singularities, and 2handle attachings along Legendrian curves.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2004
 arXiv:
 arXiv:math/0402290
 Bibcode:
 2004math......2290I
 Keywords:

 Mathematics  Geometric Topology;
 57M50;
 55R25
 EPrint:
 17 pages, 9 figures