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Blowing-Up and Whitney (a)-Regularity

Published online by Cambridge University Press:  20 November 2018

Tzee-Char Kuo ,
David J. A. Trotman  and
Li Pei Xin
Tzee-Char Kuo
Affiliation:
Department of Pure Mathematics University of Sydney Sydny, NSW 2006, Australia
David J. A. Trotman
Affiliation:
Université de Paris-Sud, Mathématiques Bâtement 425 91405, Orsay Cedex, France
Li Pei Xin
Affiliation:
Mathematics Institute Academia Sinica Beijing, China
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Abstract

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When a pair of adjacent C1 strata (X, Y) is Whitney (a)- regular at a point , there is, up to homeomorphism, just one germ at 0 of intersections S ∩ X where S is a Lipschitz transversal to Y at 0 (S is the graph of a Lipschitz map from The proof uses a blowing-up construction and a strong form of Verdier's (w)-regularity.

Keywords

58A35
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 4 , 01 December 1989 , pp. 482 - 485
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Cartan, H., Differential Calculus, Hermann, Paris, 1971.Google Scholar
2. Kuo, T.-C., On Thorn-Whitney stratification theory, Math. Ann. 234 (1978), 97–107.Google Scholar
3. Trotman, D. J. A., Transverse transversals and homeomorphic transversals, Topology 24 (1985), 25–39.Google Scholar
4. Verdier, J.-L., Stratifications de Whitney et théorème de Bertini-Sard, Inventiones Math. 36 (1976), 265–312.Google Scholar