 
Summary: arXiv:1112.0519v1[math.GT]2Dec2011
STABILIZATIONS VIA LEFSCHETZ FIBRATIONS AND
EXACT OPEN BOOKS
SELMAN AKBULUT AND M. FIRAT ARIKAN
Abstract. We show that if a contact open book (, h) on a (2n+1)manifold M (n 1)
is induced by a Lefschetz fibration : W D2
, then there is a onetoone correspondence
between positive stabilizations of (, h) and positive stabilizations of . More precisely,
any positive stabilization of (, h) is induced by the corresponding positive stabilization
of , and conversely any positive stabilization of induces the corresponding positive
stabilization of (, h). We define exact open books as boundary open books of exact
Lefschetz fibrations, and show that any exact open book carries a contact structure.
Moreover, we prove that there is a onetoone correspondence (similar to the one above)
between convex stabilizations of an exact open book and convex stabilizations of the
corresponding exact Lefschetz fibration. We also show that convex stabilization of exact
Lefschetz fibrations produces symplectomorphic manifolds.
1. Introduction
In the last decade the correspondence given by Giroux [11], between contact structures
and open book decompositions have led to many developments in understanding the rela
tions between the contact geometry and the topology of the underlying odd dimensional
