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Complex monodromy and the topology of real algebraic sets

Published online by Cambridge University Press:  04 December 2007

CLINT McCRORY
Affiliation:
University of Georgia Department of Mathematics, Athens, GA 30602, USA
ADAM PARUSIŃSKI
Affiliation:
Départment de mathématiques, Université d‘Angers, 2 bd. Lavoisier, F-49045 Angers Cedex, France School of Mathematics and Statistics, University of Sydney, Sydney NSW 2006, Australia
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Abstract

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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 Coste and Kurdyka 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.

Type
Research Article
Copyright
© 1997 Kluwer Academic Publishers