On the Fukaya-Seidel categories of surface Lefschetz fibrations

2016/07/08 by Satoshi Sugiyama, Sugiyama, Satoshi
Mathematics · #53D37 (Primary) #57M50 (Secondary) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1607.02263

openalex publication_date 2016/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a positive allowable Lefschetz fibration, PALF in short, admits a structure of exact Lefschetz fibration in the sense of Seidel \citeSe08. If the two-fold first Chern class of the total space is zero, we obtain the Fukaya-Seidel category. We prove that the derived Fukaya-Seidel category of PALF is independent of the choice of the symplectic structure. At the end of this paper, we study examples and show that derived Fukaya-Seidel categories have more information than the Milnor lattices of PALFs.

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