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We review the recent construction and basic properties of a refinement ofsutured Floer homology given by the authors in [1], defined for weakly balanced su-tured manifolds (X, Ï), and provide calculations that illustrate the differencesfrom theoriginal construction by Juh Ìasz [9]. For any weakly balanced sutured manifold (X, Ï)we construct an algebraAÏassociated to its boundary and introduce a chain complexCF(X, Ï) with coefficients inAÏ. Thefilteredchain homotopy type of CF(X, Ï) isan invariant of the sutured manifold (X, Ï). In this paper we review some of the re-sults from [1], on which the second author spoke at 2013 G Ìokova Geometry/TopologyConference.
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