The h-principle for broken Lefschetz fibrations

Details The h-principle for broken Lefschetz fibrations The h-principle for broken Lefschetz fibrations

2009-05-04

arxiv.org/abs/0905.0502v2

Mathematics

Geometric Topology

46 pages, submitted to Geometry & Topology. Corrected various typos, and a new section 4.0.2 gives uniqueness independent of h

Scientific paper

It is known that an arbitrary smooth, oriented 4-manifold admits the structure of what is called a broken Lefschetz fibration. Given a broken fibration, there are certain modifications, realized as homotopies of the fibration map, that enable one to construct infinitely many distinct fibrations of the same manifold. The aim of this paper is to prove that these modifications are sufficient to obtain every broken fibration in a given homotopy class of smooth maps. One notable application is that adding an additional "projection" move generates all broken fibrations, regardless of homotopy class. The paper ends with further applications and open problems.

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