Journal of Differential Geometry

Semialgebraic Sard Theorem for Generalized Critical Values

K. Kurdyka, P. Orro, and S. Simon

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We prove that a semialgebraic differentiable mapping has a generalized critical values set of measure zero. Moreover, if the mapping is C2 we obtain, by a generalisation of Ehresmann's fibration theorem due to P. J. Rabier [20], a locally trivial fibration over the complement of this set. In the complex case, we prove that the set of generalized critical values of a polynomial mapping is a proper algebraic set.

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J. Differential Geom., Volume 56, Number 1 (2000), 67-92.

First available in Project Euclid: 20 July 2004

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Kurdyka, K.; Orro, P.; Simon, S. Semialgebraic Sard Theorem for Generalized Critical Values. J. Differential Geom. 56 (2000), no. 1, 67--92. doi:10.4310/jdg/1090347525.

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