We introduce a refinement of the OzsváthSzabó complex
associated to a balanced sutured manifold (X,τ) by Juhász [].
An algebra \Ring_{τ} is associated to the boundary of a sutured manifold and
a filtration of its generators by \Ht^{2}(X,∂X;\Z) is defined.
For a fixed class \spinc of a \SpinC structure over the manifold
\ovl X, which is obtained from X by filling out the sutures,
the OzsváthSzabó chain complex \CFT(X,τ,\spinc)
is then defined as a chain complex with coefficients in \Ring_{τ} and
filtered by \SpinC(X,τ). The filtered chain homotopy type
of this chain complex is an invariant of (X,τ) and the
\SpinC class \spinc ∈ \SpinC(\ovl X). The construction
generalizes the construction of Juhász. It plays the role of
\CFT^{−}(X,\spinc) when X is a closed threemanifold, and
the role of
\CFKT^{−}(Y,K;\spinc)= 
⊕
\relspinc ∈ \spinc

\CFKT^{−}(Y,K,\relspinc), 

when the sutured manifold is obtained from a knot K inside a threemanifold Y.
Our invariants generalize both the knot invariants of
OzsváthSzabó and Rasmussen and the link invariants of Ozsváth and Szabó.
We study some of the basic properties of the corresponding OzsváthSzabó
complex, including the exact triangles, and some form of stabilization.
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