Multisections of Lefschetz fibrations and topology of symplectic 4-manifolds

作者：Baykur R Inanc^*; Hayano Kenta

来源：Geometry and Topology, 2016, 20(4): 2335-2395.

DOI：10.2140/gt.2016.20.2335

We initiate a study of positive multisections of Lefschetz fibrations via positive factorizations in framed mapping class groups of surfaces. Using our methods, one can effectively capture various interesting symplectic surfaces in symplectic 4-manifolds as multisections, such as Seiberg-Witten basic classes and exceptional classes, or branched loci of compact Stein surfaces as branched coverings of the 4-ball. Various problems regarding the topology of symplectic 4-manifolds, such as the smooth classification of symplectic Calabi-Yau 4-manifolds, can be translated to combinatorial problems in this manner. After producing special monodromy factorizations of Lefschetz pencils on symplectic Calabi-Yau homotopy K3 and Enriques surfaces, and introducing monodromy substitutions tailored for generating multisections, we obtain several novel applications, allowing us to construct: new counterexamples to Stipsicz's conjecture on fiber sum indecomposable Lefschetz fibrations, nonisomorphic Lefschetz pencils of the same genera on the same new symplectic 4-manifolds, the very first examples of exotic Lefschetz pencils, and new exotic embeddings of surfaces.

• 出版日期2016