Topology of real Milnor fibration for non-isolated singularities

2012/11/27 by Dutertre, Nicolas, Santos, Raimundo N. Araújo Dos
#Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1211.6233

Abstract

We consider a real analytic map F=(f₁,...,f_k) : (ℝⁿ,0) → (ℝ^k,0), 2 ≤ k ≤ n-1, that satisfies Milnor's conditions (a) and (b) introduced by D. Massey. This implies that every real analytic f_I=(f_i1,...,f_il) : (ℝⁿ,0) → (ℝ^l,0), induced from F by projections where 1 ≤ l ≤ n-2 and I=\i₁,...,i_l\, also satisfies Milnor's conditions (a) and (b). We give several relations between the Euler characteristics of the Milnor fibre of F, the Milnor fibres of the maps f_I, the link of F^-1(0) and the links of f_I^-1(0).

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