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Paper   IPM / M / 16151
School of Mathematics
  Title:   On the construction of the sutured Floer complex
  Author(s):  Eaman Eftekhary (Joint with A. Alishahi)
  Status:   In Proceedings
  Proceeding: Proceedings of the Gokova Geometry-topology conference 2013
  Year:  2021
  Pages:   97-109
  Supported by:  IPM
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, τ), and provide calculations that illustrate the differencesfrom theoriginal construction by Juh ́asz [9]. For any weakly balanced sutured manifold (X, τ)we construct an algebraAτassociated to its boundary and introduce a chain complexCF(X, τ) with coefficients inAτ. Thefilteredchain homotopy type of CF(X, τ) isan invariant of the sutured manifold (X, τ). In this paper we review some of the re-sults from [1], on which the second author spoke at 2013 G ̈okova Geometry/TopologyConference.

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