Whitney regularity and generic wings

V. Navarro Aznar; David J. A. Trotman

Annales de l'institut Fourier (1981)

  • Volume: 31, Issue: 2, page 87-111
  • ISSN: 0373-0956

Abstract

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Given adjacent subanalytic strata ( X , Y ) in R n verifying Kuo’s ratio test ( r ) (resp. Verdier’s ( w ) -regularity) we find an open dense subset of the codimension k C 1 submanifolds W (wings) containing Y such that ( X ∩ W , Y ) is generically Whitney ( b π ) -regular is exactly one more than the dimension of the set of limits of vectors for which ( b π ) fails. A general position argument for smooth strata is also given.

How to cite

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Aznar, V. Navarro, and Trotman, David J. A.. "Whitney regularity and generic wings." Annales de l'institut Fourier 31.2 (1981): 87-111. <http://eudml.org/doc/74499>.

@article{Aznar1981,
abstract = {Given adjacent subanalytic strata $(X,Y)$ in $\{\bf R\}^n$ verifying Kuo’s ratio test $(r)$ (resp. Verdier’s $(w)$-regularity) we find an open dense subset of the codimension $k$$C^1$ submanifolds $W$ (wings) containing $Y$ such that $(X\cap W,Y)$ is generically Whitney $(b^\pi )$-regular is exactly one more than the dimension of the set of limits of vectors for which $(b^\pi )$ fails. A general position argument for smooth strata is also given.},
author = {Aznar, V. Navarro, Trotman, David J. A.},
journal = {Annales de l'institut Fourier},
keywords = {adjacent subanalytic strata; test; Verdier's (w)-regularity; Whitney -regular; stratification},
language = {eng},
number = {2},
pages = {87-111},
publisher = {Association des Annales de l'Institut Fourier},
title = {Whitney regularity and generic wings},
url = {http://eudml.org/doc/74499},
volume = {31},
year = {1981},
}

TY - JOUR
AU - Aznar, V. Navarro
AU - Trotman, David J. A.
TI - Whitney regularity and generic wings
JO - Annales de l'institut Fourier
PY - 1981
PB - Association des Annales de l'Institut Fourier
VL - 31
IS - 2
SP - 87
EP - 111
AB - Given adjacent subanalytic strata $(X,Y)$ in ${\bf R}^n$ verifying Kuo’s ratio test $(r)$ (resp. Verdier’s $(w)$-regularity) we find an open dense subset of the codimension $k$$C^1$ submanifolds $W$ (wings) containing $Y$ such that $(X\cap W,Y)$ is generically Whitney $(b^\pi )$-regular is exactly one more than the dimension of the set of limits of vectors for which $(b^\pi )$ fails. A general position argument for smooth strata is also given.
LA - eng
KW - adjacent subanalytic strata; test; Verdier's (w)-regularity; Whitney -regular; stratification
UR - http://eudml.org/doc/74499
ER -

References

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