Fibred Multilinks and Singularities F G

نویسنده

  • Anne Pichon
چکیده

Milnor’s fibration theorem in [19, 20] states that if (R, 0) f → (R, 0) is the germ of a real analytic map with an isolated critical point at the origin, then for every sufficiently small sphere Sε = ∂Bε around 0 ∈ R n+k one has that the complement Sε \K of the link K = f(0) ∩ Sε fibres over the circle S . The proof of this result is by noticing first that for δ > 0 sufficiently small the tube f(Sδ) ∩ Bε fibres over the circle S 1 δ ⊂ C of radius δ, and then constructing a vector field that ”inflates” this tube taking it into the complement of (a regular neighbourhood of) the link in the sphere. When the map f is from C into C and is holomorphic, Milnor shows that one actually has a much richer structure:

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تاریخ انتشار 2005