2015/04/03 by Paul Biran, Biran, Paul, Octav Cornea +1
Mathematics · #Advanced Combinatorial Mathematics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1504.00922
openalex publication_date 2015/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a symplectic manifold (M2n,ω) we study Lagrangian cobordisms V⊂ 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⊂ 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.