On the Euler characteristic of fibres of real polynomial maps

Adam Parusiński; Zbigniew Szafraniec

ArticleOriginal scientific text

Title

On the Euler characteristic of fibres of real polynomial maps

Authors ¹, ²

Affiliations

Departement de Mathématiques, Université d'Angers, 2, bd. Lavoisier, 49045 Angers Cedex 01, France
Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

Abstract

Let Y be a real algebraic subset of

^m

and

F : Y \to^{n}

be a polynomial map. We show that there exist real polynomial functions

g_{1}, ..., g_{s}

on

^n

such that the Euler characteristic of fibres of

F

is the sum of signs of

g_{i}

.

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Title

On the Euler characteristic of fibres of real polynomial maps

Affiliations

Abstract

Bibliography