New York Journal of Mathematics
Volume 20 (2014) 1161-1173


Kyle Larson

Generic fibrations around multiple fibers

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Published: December 1, 2014
Keywords: Torus surgery, broken Lefschetz fibration, 4-manifolds
Subject: Primary: 57M50; secondary: 32S50, 57R65

Given some type of fibration on a 4-manifold X with a torus regular fiber T, we may produce a new 4-manifold XT by performing torus surgery on T. There is a natural way to extend the fibration to XT, but a multiple fiber (nongeneric) singularity is introduced. We construct explicit generic fibrations (with only indefinite fold singularities) in a neighborhood of this multiple fiber. As an application this gives explicit constructions of broken Lefschetz fibrations on all elliptic surfaces (e.g., the family E(n)p,q). As part of the construction we produce generic fibrations around exceptional fibers of Seifert fibered spaces.


The author was partially supported by NSF grant DMS-1148490.

Author information

Department of Mathematics, University of Texas at Austin, Austin, TX, USA