\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
We introduce a refinement of the Ozsv\'ath-Szab\'o complex
associated to a balanced sutured manifold $(X,\tau)$ by Juh\'asz \cite{Juh}.
An algebra $\Ring_\tau$ is associated to the boundary of a sutured manifold and
a filtration of its generators by $\Ht^2(X,\partial X;\Z)$ 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 Ozsv\'ath-Szab\'o chain complex $\CFT(X,\tau,\spinc)$
is then defined as a chain complex with coefficients in $\Ring_\tau$ and
filtered by $\SpinC(X,\tau)$. The filtered chain homotopy type
of this chain complex is an invariant of $(X,\tau)$ and the
$\SpinC$ class $\spinc\in\SpinC(\ovl X)$. The construction
generalizes the construction of Juh\'asz. It plays the role of
$\CFT^{-}(X,\spinc)$ when $X$ is a closed three-manifold, and
the role of
$$\CFKT^-(Y,K;\spinc)=\bigoplus_{\relspinc\in\spinc}\CFKT^-(Y,K,\relspinc),$$
when the sutured manifold is obtained from a knot $K$ inside a three-manifold $Y$.
Our invariants generalize both the knot invariants of
Ozsv\'ath-Szab\'o and Rasmussen and the link invariants of Ozsv\'ath and Szab\'o.
We study some of the basic properties of the corresponding Ozsv\'ath-Szab\'o
complex, including the exact triangles, and some form of stabilization.
\end{document}