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A refinement of sutured floer homology

Alishahi, A. S ; Sharif University of Technology | 2015

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  1. Type of Document: Article
  2. Publisher: International Press of Boston, Inc , 2015
  3. Abstract:
  4. We introduce a refinement of the Ozsváth-Szabó complex associated by Juhósz [Ju1] to a balanced sutured manifold (X,τ). An algebra (Formula Presented)τ is associated to the boundary of a sutured manifold. For a fixed class s of a Spinc structure over the manifold X, which is obtained from (Formula Presented) by filling out the sutures, the Ozsvóth-Szabó chain complex CF(X, τ, s) is then defined as a chain complex with coefficients in (Formula Presented)T and filtered by the relative Spinc classes in Spinc(X, τ). The filtered chain homotopy type of this chain complex is an invariant of (X,τ) and the Spinc class s Є Spinc(Formula Presented). The construction generalizes the construction of Juhasz. It plays the role of CF-(X, s)when X is a closed three-manifold, and the role of (Formula Presented) when the sutured manifold is obtained from a knot K inside a three-manifold Y. Our invariants thus generalize both the knot invariants of Ozsvóth-Szabó and Rasmussen and the link invariants of Ozsvóth and Szabó. We study some of the basic properties of the Ozsváth-Szabó complex corresponding to a balanced sutured manifold, including the behaviour under boundary connected sum, some form of stabilization for the complex, and an exact triangle generalizing the surgery exact triangles for knot Floer complexes
  5. Keywords:
  7. Source: Journal of Symplectic Geometry ; Volume 13, Issue 3 , 2015 , Pages 609-743 ; 15275256 (ISSN)
  8. URL: https://arxiv.org/abs/1112.3540