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arXiv · 1607.02263

On the Fukaya-Seidel categories of surface Lefschetz fibrations

Satoshi Sugiyama
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Abstract

We prove that a positive allowable Lefschetz fibration, PALF in short, admits a structure of exact Lefschetz fibration in the sense of Seidel \cite{Se08}. 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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Satoshi Sugiyama. 2016-07-08. On the Fukaya-Seidel categories of surface Lefschetz fibrations. https://arxiv.org/abs/1607.02263

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