Niveau: Supérieur, Doctorat, Bac+8
J. London Math. Soc. (2) 80 (2009) 311–325 C!2009 London Mathematical Society doi:10.1112/jlms/jdp027 Milnor fibrations of meromorphic functions Arnaud Bodin, Anne Pichon and Jose Seade Abstract In analogy with the holomorphic case, we compare the topology of Milnor fibrations associated to a meromorphic germ f/g: the local Milnor fibrations given on Milnor tubes over punctured discs around the critical values of f/g, and the Milnor fibration on a sphere. 1. Introduction The classical fibration theorem of Milnor in [6] says that every holomorphic map (germ) f : (Cn, 0) ? (C, 0) with n ! 2 and a critical point at 0 ? Cn has two naturally associated fibre bundles, and both of these are equivalent. The first is ? = f |f | : S? \K ?? S1, (1) where S? is a sufficiently small sphere around 0 ? Cn and K = f?1(0) ? S? is the link of f at 0. The second fibration is f : B? ? f?1(∂D?) ?? ∂D? ?= S1, (2) where B? is the closed ball in Cn with boundary S? and D? is a disc around 0 ? C, which is sufficiently small with respect to ?.
- truncated global
- milnor's proof concerns
- fibre bundle
- see also
- global milnor
- naturally associated
- meromorphic germ
- fibration over
- milnor fibration