On genus-1 simplified broken lefschetz fibrations

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


Auroux, Donaldson and Katzarkov introduced broken Lefschetz fibrations as a generalization of Lefschetz fibrations in order to describe near-symplectic 4-manifolds. We first study monodromy representations of higher sides of genus-1 simplified broken Lefschetz fibrations. We then completely classify diffeomorphism types of such fibrations with connected fibers and with less than six Lefschetz singularities. In these studies, we obtain several families of genus-1 simplified broken Lefschetz fibrations, which we conjecture contain all such fibrations, and determine the diffeomorphism types of the total spaces of these fibrations. Our results are generalizations of Kas' classification theorem of genus-1 Lefschetz fibrations, which states that the total space of a nontrivial genus-1 Lefschetz fibration over S2 is diffeomorphic to an elliptic surface E.n/ for some n ≤ 1.

Original languageEnglish
Pages (from-to)1267-1322
Number of pages56
JournalAlgebraic and Geometric Topology
Issue number3
Publication statusPublished - 2011
Externally publishedYes

ASJC Scopus subject areas

  • Geometry and Topology


Dive into the research topics of 'On genus-1 simplified broken lefschetz fibrations'. Together they form a unique fingerprint.

Cite this