Generic fibrations around multiple fibers

zbMATH Open1334.57014arXiv1405.6418MaRDI QIDQ2339299

Kyle Larson

Publication date: 31 March 2015

Published in: The New York Journal of Mathematics (Search for Journal in Brave)

Abstract: Given some type of fibration on a 4-manifold $X$ with a torus regular fiber $T$, we may produce a new 4-manifold $X_T$ by performing torus surgery on $T$. There is a natural way to extend the fibration to $X_T$, but a multiple fiber (non-generic) 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.

Full work available at URL: https://arxiv.org/abs/1405.6418

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zbMATH Keywords

4-manifoldbroken Lefschetz fibrationround handlelogarithmic transformtorus surgery

Mathematics Subject Classification ID

General geometric structures on low-dimensional manifolds (57M50) Surgery and handlebodies (57R65) Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants (32S50)

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