Topology of real Milnor fibration for non-isolated singularities

We consider a real analytic map $F=(f_1,…,f_k) : ($\mathbb{R}$^n,0) \rightarrow ($\mathbb{R}$^k,0)$,$2 \le k \le n-1$, that satisfies Milnor’s conditions (a) and (b) introduced by D. Massey. This implies that every real analytic $f_I=(f_{i_1},…,f_{i_l}) : ($\mathbb{R}$^n,0) \rightarrow ($\mathbb{R}$^l,0)$,inducedfrom$F$byprojectionswhere$1 \le l \le n-2$and$I={i_1,…,i_l}$, 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 $f_I^{-1}(0)$.