Multisections of lefschetz fibrations and topology of symplectic 4–manifolds

R. İnanç Baykur, Kenta Hayano

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)2335-2395
Number of pages61
JournalGeometry and Topology
Volume20
Issue number4
DOIs
Publication statusPublished - 2016 Sep 15

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Lefschetz Fibration
Topology
Monodromy
Factorization
Branched Covering
Mapping Class Group
Combinatorial Problems
Homotopy
Locus
Substitution
Counterexample
Genus
Fiber

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Multisections of lefschetz fibrations and topology of symplectic 4–manifolds. / Baykur, R. İnanç; Hayano, Kenta.

In: Geometry and Topology, Vol. 20, No. 4, 15.09.2016, p. 2335-2395.

Research output: Contribution to journalArticle

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