COMPLEX MONODROMY AND THE TOPOLOGY OF REAL ALGEBRAIC-SETS

A relation between the Euler characteristics of the Milnor fibres of a real analytic function is derived from a simple identity involving co mplex monodromy and complex conjugation. A corollary is the result of Coste and Kurdyka that the Euler characteristic of the local link of a n irreducible algebraic subset of a real algebraic set is generically constant module 4. A similar relation for iterated Milnor fibres of or dered sets of functions is used to define topological invariants of or dered collections of algebraic subsets.