Heegaard Floer Homology and the Topology of Three Manifolds, Ph.D. Dissertation Sharif University of Technology ; Bahraini, Alireza (Supervisor) ; Eftekhary, Eaman (Supervisor)
Abstract
We introduce a refinement of the Ozsváth-Szabó complex associated by Juhász [8] to a balanced sutured manifold (X; ). An algebra A 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 X by filling out the sutures, the Ozsváth-Szabó chain complex CF(X; ; s) is then defined as a chain complex with coefficients in A and filtered by the relative Spinc classes in Spinc(X; ). The filtered chain homotopy type of this chain complex is an invariant of (X; ) and the Spinc class s 2 Spinc(X). The construction generalizes the construction of Juhász. It plays the role of CF (X; s) when X is a closed three-manifold,...
Cataloging briefHeegaard Floer Homology and the Topology of Three Manifolds, Ph.D. Dissertation Sharif University of Technology ; Bahraini, Alireza (Supervisor) ; Eftekhary, Eaman (Supervisor)
Abstract
We introduce a refinement of the Ozsváth-Szabó complex associated by Juhász [8] to a balanced sutured manifold (X; ). An algebra A 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 X by filling out the sutures, the Ozsváth-Szabó chain complex CF(X; ; s) is then defined as a chain complex with coefficients in A and filtered by the relative Spinc classes in Spinc(X; ). The filtered chain homotopy type of this chain complex is an invariant of (X; ) and the Spinc class s 2 Spinc(X). The construction generalizes the construction of Juhász. It plays the role of CF (X; s) when X is a closed three-manifold,...
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