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Complex monodromy and the topology of real algebraic sets

Published online by Cambridge University Press:  04 December 2007

CLINT McCRORY  and
ADAM PARUSIŃSKI
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.

Keywords

Milnor fibremonodromyEuler characteristicreal algebraic setlink
Type
Research Article
Information
Compositio Mathematica , Volume 106 , Issue 2 , April 1997 , pp. 211 - 233
Copyright
© 1997 Kluwer Academic Publishers