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A STABLE CLASSIFICATION OF LEFSCHETZ DENIS AUROUX
 

Summary: A STABLE CLASSIFICATION OF LEFSCHETZ
FIBRATIONS
DENIS AUROUX
Abstract. We study the classification of Lefschetz fibrations up to sta-
bilization by fiber sum operations. We show that for each genus there is
a "universal" fibration f0
g with the property that, if two Lefschetz fibra-
tions over S2
have the same Euler-PoincarŽe characteristic and signature,
the same numbers of reducible singular fibers of each type, and admit
sections with the same self-intersection, then after repeatedly fiber sum-
ming with f0
g they become isomorphic. As a consequence, any two com-
pact integral symplectic 4-manifolds with the same (c2
1, c2, c1 ·[], []2
)
become symplectomorphic after blowups and symplectic sums with f0
g .
1. Introduction
Lefschetz fibrations have been the focus of a lot of attention ever since

  

Source: Auroux, Denis - Department of Mathematics, Massachusetts Institute of Technology (MIT)

 

Collections: Mathematics