A new construction of the Fukaya-Seidel category associated with a symplectic Lefschetz fibration is outlined.Applying this construction in an infinite dimensional case, a Fukaya-Seidel-type category is associated with a smooth three-manifold.In this case the construction is based on a five-dimensional gauge theory.152 Andriy Haydys 4.2 Dimension three 191 5 Invariants 196 Appendix A Pseudoholomorphic strips and pseudoholomorphic planes 198
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