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Complex monodromy and the topology of real algebraic sets. (English) Zbl 0949.14037

Summary: A relation between the Euler characteristics of the Milnor fibres of a real analytic function is derived from a simple identity involving complex monodromy and complex conjugation. A corollary is the result of M. Coste and K. Kurdyka [Topology 31, No. 2, 323-336 (1992; Zbl 0787.14038)] that the Euler characteristic of the local link of an irreducible algebraic subset of a real algebraic set is generically constant modulo 4. A similar relation for iterated Milnor fibres of ordered sets of functions is used to define topological invariants of ordered collections of algebraic subsets.

MSC:

14P25 Topology of real algebraic varieties
32S50 Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants
14F45 Topological properties in algebraic geometry

Citations:

Zbl 0787.14038
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