Open Access
Translator Disclaimer
2011 On genus–$1$ simplified broken Lefschetz fibrations
Kenta Hayano
Algebr. Geom. Topol. 11(3): 1267-1322 (2011). DOI: 10.2140/agt.2011.11.1267


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 n1.


Download Citation

Kenta Hayano. "On genus–$1$ simplified broken Lefschetz fibrations." Algebr. Geom. Topol. 11 (3) 1267 - 1322, 2011.


Received: 25 November 2010; Revised: 3 February 2011; Accepted: 14 February 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1229.57017
MathSciNet: MR2801419
Digital Object Identifier: 10.2140/agt.2011.11.1267

Primary: 57M50
Secondary: 32S50 , 57R65

Keywords: $4$–manifold , broken Lefschetz fibration , chart description , Kirby diagram , monodromy representation

Rights: Copyright © 2011 Mathematical Sciences Publishers


Vol.11 • No. 3 • 2011
Back to Top