Singular fibrations over surfaces - Archive ouverte HAL Accéder directement au contenu
Chapitre D'ouvrage Année : 2023

Singular fibrations over surfaces

Louis Funar

Résumé

Singular fibrations generalize achiral Lefschetz fibrations of 4-manifolds over surfaces while sharing some of their properties. For instance, relatively minimal singular fibrations are determined by their monodromy. We explain how to construct examples of singular fibrations with a single singularity and Matsumoto's construction of singular fibrations of the sphere $S^4$. Previous results of Hirzebruch and Hopf on 2-plane fields with finitely many singularities are outlined in connection with the work of Neumann and Rudolph on the Hopf invariant. Eventually, we prove that closed orientable 4-manifolds with large first Betti number and vanishing second Betti number do not admit singular fibrations.

Dates et versions

hal-03798296 , version 1 (05-10-2022)

Identifiants

Citer

Louis Funar. Singular fibrations over surfaces. A. Papadopoulos. Essays in Geometry- Dedicated to Norbert A'Campo, European Mathematical Society Publishing House, pp.515-556, 2023, IRMA Lectures Math. Theor. Phys. 34. ⟨hal-03798296⟩

Collections

UGA CNRS FOURIER
9 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More