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A
–dimensional open
book
determines a
closed, oriented
–manifold
and a contact
structure
on
. The contact
structure
is
Stein fillable if
is
positive, ie
can be written as a product of right-handed Dehn twists. Work of Wendl implies that
when
has genus zero the converse holds, that is
On the other hand, results by Wand [Phd thesis (2010)] and by Baker,
Etnyre and Van Horn–Morris [J. Differential Geom. 90 (2012) 1-80]
imply the existence of counterexamples to the above implication with
of arbitrary genus strictly greater than one. The main purpose of this
paper is to prove the implication holds under the assumption that
is a one-holed torus
and
is a Heegaard
Floer
–space.
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