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Transversality of smooth definable maps in O-minimal structures

Part of: Calculus on manifolds; nonlinear operators

Published online by Cambridge University Press:  10 January 2019

NHAN NGUYEN  and
SAURABH TRIVEDI
NHAN NGUYEN
Affiliation:
ICMC-University of Sao Paulo
SAURABH TRIVEDI*
Affiliation:
ICMC-University of Sao Paulo
*
e-mails: nguyenxuanvietnhan@gmail.com, saurabh.trivedi@gmail.com
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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

Secondary: 58C25: Differentiable maps 14P10: Semialgebraic sets and related spaces
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

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References

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