On genus-1 simplified broken lefschetz fibrations

研究成果: Article

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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.

元の言語English
ページ(範囲)1267-1322
ページ数56
ジャーナルAlgebraic and Geometric Topology
11
発行部数3
DOI
出版物ステータスPublished - 2011 7 29
外部発表Yes

ASJC Scopus subject areas

  • Geometry and Topology

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