Fibrations structure and degree formulae for Milnor fibers

Nicolas Dutertre (1, 2) , Raimundo N. Araújo dos Santos (3) , Ying Chen (4) , Antonio Andrade (4)

1 I2M - Institut de Mathématiques de Marseille
2 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
3 ICMC-USP - Instituto de Ciências Mathemàticas e de Computação [São Carlos]
4 Instituto de Ciencias Matematicas e de Computaçao

In this survey, we remind some fibrations structure theorems (also called Milnor's fibrations) recently proved in the real and complex case, in the local and global settings. We give several Poincaré-Hopf type formulae which relates the Euler-Poincaré characteristic of these fibers (also called Milnor's fibers) and indices (topological degree) of appropriated vector fields defined on spheres of radii small or big enough.

Domaines: Géométrie algébrique [math.AG]; Topologie géométrique [math.GT]

Nicolas Dutertre, Raimundo N. Araújo dos Santos, Ying Chen, Antonio Andrade. Fibrations structure and degree formulae for Milnor fibers. RIMS Kokyuroku Bessatsu, 2016, Theory of singularities of smooth mappings and around it B55, pp.41-65. ⟨hal-01064938⟩