Journal of Differential Geometry

Semialgebraic Sard Theorem for Generalized Critical Values

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

Full-text: Open access

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 20 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090347525

Digital Object Identifier
doi:10.4310/jdg/1090347525

Mathematical Reviews number (MathSciNet)
MR1863021

Zentralblatt MATH identifier
1067.58031

Citation

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. https://projecteuclid.org/euclid.jdg/1090347525


Export citation