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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Stratified transversality by isotopy


Authors: C. Murolo, D. J. A. Trotman and A. A. Du Plessis
Journal: Trans. Amer. Math. Soc. 355 (2003), 4881-4900
MSC (2000): Primary 58A35, 57N75; Secondary 57N80, 57R52
Published electronically: July 28, 2003
MathSciNet review: 1997589
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Abstract | References | Similar Articles | Additional Information

Abstract: For $\mathcal{X} $ an abstract stratified set or a $(w)$-regular stratification, hence for any $(b)$-, $(c)$- or $(L)$-regular stratification, we prove that after stratified isotopy of $\mathcal{X} $, a stratified subspace $\mathcal{W}$ of $\mathcal{X} $, or a stratified map $h : \mathcal{Z} \to \mathcal{X}$, can be made transverse to a fixed stratified map $ g: \mathcal{Y} \to \mathcal{X}$.


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Additional Information

C. Murolo
Affiliation: Laboratoire d’Analyse, Topologie et Probabilités, Centre de Mathématiques et Informatique, Université de Provence, 39, rue Joliot-Curie, 13453 Marseille Cedex 13, France
Email: murolo@gyptis.univ-mrs.fr

D. J. A. Trotman
Affiliation: Laboratoire d’Analyse, Topologie et Probabilités, Centre de Mathématiques et Informatique, Université de Provence, 39, rue Joliot-Curie, 13453 Marseille Cedex 13, France
Email: trotman@gyptis.univ-mrs.fr

A. A. Du Plessis
Affiliation: Matematisk Institut, Ny Munkegade, Universitet Aarhus, Aarhus, Denmark
Email: matadp@mi.aau.dk

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03236-7
PII: S 0002-9947(03)03236-7
Received by editor(s): October 2, 2001
Received by editor(s) in revised form: June 4, 2002
Published electronically: July 28, 2003
Additional Notes: The first author received support from the Department of Mathematics of the Faculty of Engineering and the Office of International Relations of the University of Naples.
Article copyright: © Copyright 2003 American Mathematical Society