Abstract
Given a symplectic manifold M we study Lagrangian cobordisms \(V\subset E\) where E is the total space of a Lefschetz fibration having M as generic fiber. We prove a generation result for these cobordisms in the appropriate derived Fukaya category. As a corollary, we analyze the relations among the Lagrangian submanifolds \(L\subset M\) that are induced by these cobordisms. This leads to a unified treatment—and a generalization—of the two types of relations among Lagrangian submanifolds of M that were previously identified in the literature: those associated to Dehn twists that were discovered by Seidel (Topology 42(5):1003–1063, 2003) and the relations induced by cobordisms in trivial symplectic fibrations described in our previous work (J Am Math Soc 26(2):295–340, 2013; Geom Funct Anal 24(6):1731–1830, 2014).
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