Abstract
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 language | English |
|---|---|
| Pages (from-to) | 1267-1322 |
| Number of pages | 56 |
| Journal | Algebraic and Geometric Topology |
| Volume | 11 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2011 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Geometry and Topology
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On genus-1 simplified broken lefschetz fibrations. / Hayano, Kenta.
In: Algebraic and Geometric Topology, Vol. 11, No. 3, 2011, p. 1267-1322.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On genus-1 simplified broken lefschetz fibrations
AU - Hayano, Kenta
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=79960704066&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79960704066&partnerID=8YFLogxK
U2 - 10.2140/agt.2011.11.1267
DO - 10.2140/agt.2011.11.1267
M3 - Article
VL - 11
SP - 1267
EP - 1322
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
SN - 1472-2747
IS - 3
ER -