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arXiv · 1504.00922

Lagrangian cobordism in Lefschetz fibrations

Paul Biran·Octav Cornea
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Abstract

Given a symplectic manifold $(M^{2n},\omega)$ 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 and the relations induced by cobordisms in trivial symplectic fibrations described in our previous work.

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Paul Biran, Octav Cornea. 2015-04-03. Lagrangian cobordism in Lefschetz fibrations. https://arxiv.org/abs/1504.00922

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