On the topology of a generic fibre of a polynomial function

In this work we study the topologies of the fibres of some families of comp lex polynomial functions with isolated critical points. We consider polynom ials with some transversality conditions at infinity and compute explicitly its global Milnor number mu(f), the invariant lambda(f) and therefore the Euler characteristic of its generic fibre. We show that under some mild tra nsversality condition (transversal at infinity) the behavior of f at infini ty is good and the topology of the generic fibre is determined by the two h omogeneous parts of higher degree of f. Finally we study families of polyno mials, called two-term polynomials. This polynomials may have atypical valu es at infinity. Given such a two-term polynomial I we characterize its atyp ical values by some invariants of f. These polynomials are a source of inte resting examples.