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Semi-algebraic functions with non-compact critical set

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Résumé

Let X ⊂ R^n be a closed semi-algebraic set, F : R^n → R be a C^2 semi-algebraic function and f = F |X : X → R n be the restriction of F to X. We define the global index of a critical value c_i of f and prove an index formula for χ(X) that generalizes a result previously proved by the authors for the case of isolated critical points. We define also new indices at infinity and prove an alternative index formula for χ(X).
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Dates et versions

hal-03589189 , version 1 (25-02-2022)

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  • HAL Id : hal-03589189 , version 1

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Nicolas Dutertre, Juan Antonio Moya Pérez. Semi-algebraic functions with non-compact critical set. 2022. ⟨hal-03589189⟩
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