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Transversality of smooth definable maps in O-minimal structures
Published online by Cambridge University Press: 10 January 2019
Abstract
We present a definable smooth version of the Thom transversality theorem. We show further that the set of non-transverse definable smooth maps is nowhere dense in the definable smooth topology. Finally, we prove a definable version of a theorem of Trotman which says that the Whitney (a)-regularity of a stratification is necessary and sufficient for the stability of transversality.
MSC classification
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 168 , Issue 3 , May 2020 , pp. 519 - 533
- Copyright
- Copyright © Cambridge Philosophical Society 2019