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Complex monodromy and the topology of real algebraic sets |
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| Authors: | CLINT McCRORY ADAM PARUSIŃSKI |
| Affiliation: | (1) Department of Mathematics, University of Georgia, Athens, GA 30602, USA;(2) Départment de mathématiques, Université d!["rsquo"]("/content/k6q81085677h5657/xlarge8217.gif") Angers, 2 bd. Lavoisier, F-49045 Angers Cedex, France;(3) School of Mathematics and Statistics, University of Sydney, Sydney, NSW, 2006, Australia |
| Abstract: | A relation between the Euler characteristics of the Milnorfibres of a real analytic function is derived from a simple identity involvingcomplex monodromy and complex conjugation. A corollary is the result of Costeand Kurdyka that the Euler characteristic of the local link of an irreduciblealgebraic subset of a real algebraic set is generically constant modulo 4. Asimilar relation for iterated Milnor fibres of ordered sets of functions isused to define topological invariants of ordered collections of algebraicsubsets. |
| Keywords: | Milnor fibre monodromy Euler characteristic real algebraic set link. |
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