We introduce a refinement of the Ozsváth-Szabó complex associated to a balanced sutured manifold ... more We introduce a refinement of the Ozsváth-Szabó complex associated to a balanced sutured manifold (X, τ ) by Juhász . An algebra Aτ is associated to the boundary of a sutured manifold and a filtration of its generators by H 2 (X, ∂X; Z) is defined. For a fixed class s of a Spin c structure over the manifold X, which is obtained from X by filling out the sutures, the Ozsváth-Szabó chain complex CF(X, τ, s) is then defined as a chain complex with coefficients in Aτ and filtered by Spin c (X, τ ). The filtered chain homotopy type of this chain complex is an invariant of (X, τ ) and the Spin c class s ∈ Spin c (X). The construction generalizes the construction of Juhász. It plays the role of CF − (X, s) when X is a closed three-manifold, and the role of
We introduce a refinement of the Ozsváth-Szabó complex associated to a balanced sutured manifold ... more We introduce a refinement of the Ozsváth-Szabó complex associated to a balanced sutured manifold (X, τ ) by Juhász . An algebra Aτ is associated to the boundary of a sutured manifold and a filtration of its generators by H 2 (X, ∂X; Z) is defined. For a fixed class s of a Spin c structure over the manifold X, which is obtained from X by filling out the sutures, the Ozsváth-Szabó chain complex CF(X, τ, s) is then defined as a chain complex with coefficients in Aτ and filtered by Spin c (X, τ ). The filtered chain homotopy type of this chain complex is an invariant of (X, τ ) and the Spin c class s ∈ Spin c (X). The construction generalizes the construction of Juhász. It plays the role of CF − (X, s) when X is a closed three-manifold, and the role of
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Papers by Akram Alishahi