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Geometric versions of Whitney regularity for smooth stratifications. (English) Zbl 0456.58002


MSC:

58A35 Stratified sets
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References:

[1] H. BRODERSEN and D. TROTMAN , Whitney (b)-Regularity is Weaker than Kuo’s Ratio Test for Real Algebraic Stratifications , Aarhus University preprint, November 1978 (to appear in Mathematica Scandinavia). Zbl 0425.58005 · Zbl 0425.58005
[2] C. G. GIBSON et al., Topological Stability of Smooth Mappings (Springer Lecture Notes, Vol. 552, Berlin, 1976 ). MR 55 #9151 | Zbl 0377.58006 · Zbl 0377.58006
[3] M. HIRSCH , Differential Topology , Springer-Verlag, New York, 1976 . MR 56 #6669 | Zbl 0356.57001 · Zbl 0356.57001
[4] A. KAMBOUCHNER and D. J. A. TROTMAN , Whitney (a)-Faults which are Hard to Detect (Ann. scient. Éc. Norm. Sup., Vol. 12, 1979 , pp. 473-479). Numdam | MR 81g:58002b | Zbl 0456.58003 · Zbl 0456.58003
[5] T.-C. KUO , The Ratio Test for Analytic Whitney Stratifications [Liverpool singularities symposium I (Springer Lecture Notes, Vol. 192, Berlin, 1971 , pp. 141-149)]. MR 43 #5056 | Zbl 0246.32006 · Zbl 0246.32006
[6] J. MATHER , Notes on topological stability , Harvard University, 1970 . · Zbl 0207.54303
[7] J. MATHER , Stratifications and Mappings , in Dynamical Systems (edited by M. PEIXOTO, Ed.), Academic Press, 1971 , pp. 195-223.
[8] J. R. MUNKRES , Elementary differential topology (Annals Study, Vol. 54, Princeton, 1968 ). · Zbl 0107.17201
[9] R. THOM , Propriétés différentielles locales des ensembles analytiques (Séminaire Bourbaki, No. 281, pp. 1964-1965). Numdam | Zbl 0184.31402 · Zbl 0184.31402
[10] R. THOM , Ensembles et morphismes stratifiés (Bull. Amer. Math. Soc., Vol. 75, 1969 , pp. 240-284). Article | MR 39 #970 | Zbl 0197.20502 · Zbl 0197.20502
[11] D. J. A. TROTMAN , A Transversality Property Weaker than Whitney (a)-regularity (Bull. London Math. Soc., Vol. 8, 1976 , pp. 225-228). MR 54 #11381 | Zbl 0344.57009 · Zbl 0344.57009
[12] D. J. A. TROTMAN , Geometric Versions of Whitney Regularity (Math. Proc. Camb. Phil. Soc., Vol. 80, 1976 , pp. 99-101). MR 53 #9284 | Zbl 0329.57010 · Zbl 0329.57010
[13] D. J. A. TROTMAN , Whitney Stratifications : Faults and Detectors (Thesis, Warwick University, 1977 ).
[14] D. TROTMAN , Interprétations topologiques des conditions de Whitney [Journées singulières, Dijon, juin 1978 (Astérisque, Vol. 59-60, 1979 , pp. 233-248)]. MR 81f:58005 | Zbl 0405.58006 · Zbl 0405.58006
[15] J.-L. VERDIER , Stratifications de Whitney et théorème de Bertini-Sard (Invent. Math., Vol. 36, 1976 , pp. 295-312). MR 58 #1242 | Zbl 0333.32010 · Zbl 0333.32010
[16] C. T. C. WALL , Regular Stratifications, Dynamical Systems , Warwick, 1974 (Springer Lecture Notes, No. 468, 1975 , pp. 332-344). MR 58 #31184 | Zbl 0439.58008 · Zbl 0439.58008
[17] C. T. C. WALL , Geometric Properties of Generic Differentiable Manifolds, Geometry and Topology , Rio de Janeiro, July 1976 (Springer Lecture Notes, No. 597, Berlin, 1977 , pp. 707-774). MR 58 #13144 | Zbl 0361.58004 · Zbl 0361.58004
[18] H. WHITNEY , Tangents to an Analytic Variety (Annals of Math., Vol. 81, 1965 , pp. 496-549). MR 33 #745 | Zbl 0152.27701 · Zbl 0152.27701
[19] K. WIRTHMULLER , Stratifications and flows , in [2].
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