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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Transversality theorems for the weak topology
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by Saurabh Trivedi PDF
Proc. Amer. Math. Soc. 141 (2013), 2181-2192 Request permission

Abstract:

In 1979, Trotman proved, using the techniques of the Thom transversality theorem, that under some conditions on the dimensions of the manifolds under consideration, openness of the set of maps transverse to a stratification in the strong (Whitney) topology implies that the stratification is $(a)$-regular. Here we first discuss the Thom transversality theorem for the weak topology and then give a similiar kind of result for the weak topology under very weak hypotheses. Recently, several transversality theorems have been proved for complex manifolds and holomorphic maps. In view of these transversality theorems we also prove a result analogous to Trotman’s result in the complex case.
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Additional Information
  • Saurabh Trivedi
  • Affiliation: LATP (UMR 6632), Centre de Mathématiques et Informatique, Université de Provence, 39 rue Joliot-Curie, 13013 Marseille, France
  • Address at time of publication: LATP (UMR 7353), Centre de Mathématiques et Informatique, Aix-Marseille Université, 39 rue Joliot-Curie, 13453 Marseille Cedex 13, France
  • Email: saurabh@cmi.univ-mrs.fr
  • Received by editor(s): July 13, 2011
  • Received by editor(s) in revised form: September 5, 2011, and September 28, 2011
  • Published electronically: January 11, 2013
  • Communicated by: Franc Forstneric
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 2181-2192
  • MSC (2010): Primary 58A35, 57R35; Secondary 32H02, 32Q28, 32S60
  • DOI: https://doi.org/10.1090/S0002-9939-2013-11496-6
  • MathSciNet review: 3034444