Open Access
September, 2000 Semialgebraic Sard Theorem for Generalized Critical Values
K. Kurdyka, P. Orro, S. Simon
J. Differential Geom. 56(1): 67-92 (September, 2000). DOI: 10.4310/jdg/1090347525


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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K. Kurdyka. P. Orro. S. Simon. "Semialgebraic Sard Theorem for Generalized Critical Values." J. Differential Geom. 56 (1) 67 - 92, September, 2000.


Published: September, 2000
First available in Project Euclid: 20 July 2004

zbMATH: 1067.58031
MathSciNet: MR1863021
Digital Object Identifier: 10.4310/jdg/1090347525

Rights: Copyright © 2000 Lehigh University

Vol.56 • No. 1 • September, 2000
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