Equivalence of differentiable mappings and analytic mappings
Publications Mathématiques de l'IHÉS (1981)
- Volume: 54, page 37-122
- ISSN: 0073-8301
Access Full Article
topHow to cite
topShiota, Masahiro. "Equivalence of differentiable mappings and analytic mappings." Publications Mathématiques de l'IHÉS 54 (1981): 37-122. <http://eudml.org/doc/103978>.
@article{Shiota1981,
author = {Shiota, Masahiro},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {equivalence of mappings; polynomial mapping; germ of analytic mapping; isolated topological singularities},
language = {eng},
pages = {37-122},
publisher = {Institut des Hautes Études Scientifiques},
title = {Equivalence of differentiable mappings and analytic mappings},
url = {http://eudml.org/doc/103978},
volume = {54},
year = {1981},
}
TY - JOUR
AU - Shiota, Masahiro
TI - Equivalence of differentiable mappings and analytic mappings
JO - Publications Mathématiques de l'IHÉS
PY - 1981
PB - Institut des Hautes Études Scientifiques
VL - 54
SP - 37
EP - 122
LA - eng
KW - equivalence of mappings; polynomial mapping; germ of analytic mapping; isolated topological singularities
UR - http://eudml.org/doc/103978
ER -
References
top- [1] M. ARTIN, On the solution of analytic equations, Inv. Math., 5 (1968), 277-291. Zbl0172.05301MR38 #344
- [2] J. BOCHNAK-S. ŁOJASIEWICZ, A converse of the Kuiper-Kuo Theorem, Lecture Notes in Math., Springer, 192 (1971), 254-261. Zbl0221.58002MR45 #1059
- [3] N. M. CHRISTENSON, Zur Łojasiewicz-Ungleichung für differenzierbare Funktionen, Manuscripta Math., 20 (1977), 255-262. Zbl0354.26009
- [4] M. HERVÉ, Several complex variables, Local theory, Oxford, 1963. Zbl0113.29003MR27 #1616
- [5] M. W. HIRSCH, B. C. MAZUR, Smoothings of piecewise linear manifolds, Ann. Math. Studies, 80, Princeton Univ. Press, 1974. Zbl0298.57007MR54 #3711
- [6] L. HÖRMANDER, Linear partial differential operators, Springer, 1969.
- [7] H. C. KING, Real analytic germs and their varieties at isolated singularities, Inv. Math., 37 (1976), 193-199. Zbl0318.57037MR54 #13114
- [8] R. C. KIRBY-L. C. SIEBENMANN, Foundational essays on topological manifolds, smoothings, and triangulation, Ann. Math. Studies, 88, Princeton Univ. Press, 1977. Zbl0361.57004MR58 #31082
- [9] T. C. KUO, The jet space Jr(n, p), Lecture Notes in Math., Springer, 192 (1971), 169-177. Zbl0221.58001MR43 #6939
- [10] N. LEVINSON, A canonical form for an analytic function of several variables at a critical point, Bull. Amer. Math. Soc., 66 (1960), 68-69. Zbl0192.18201MR26 #2634
- [11] N. LEVINSON, A polynomial canonical form for certain analytic functions of two variables at a critical point, Bull. Amer. Math. Soc., 66 (1960), 366-368. Zbl0192.18202MR26 #2635
- [12] B. MALGRANGE, Ideals of differentiable functions, Oxford Univ. Press, 1966. Zbl0177.17902
- [13] B. MALGRANGE, Sur les points singuliers des équations différentielles, Séminaire Goulaouic-Schwartz, 1972. Zbl0252.34031MR53 #11668
- [14] J. N. MATHER, How to stratify mapping and jet spaces, Lecture Notes in Math., Springer, 535 (1975), 128-176. Zbl0398.58008MR56 #13259
- [15] J. N. MATHER, Stability of C∞ mappings, III. Finitely determined map germs, Publ. Math. I.H.E.S., 35 (1968), 127-156. Zbl0159.25001MR43 #1215a
- [16] E. E. MOISE, Affine structures in 3-manifolds V. The triangulation theorem and Hauptvermutung, Ann. Math., 56 (1952), 96-114. Zbl0048.17102MR14,72d
- [17] E. E. MOISE, Geometric topology in dimension 2 and 3, GTM, Springer, 1977. Zbl0349.57001MR58 #7631
- [18] J. R. MUNKRES, Obstructions to the smoothing of piecewise differentiable structures, Ann. Math., 72 (1960), 521-554. Zbl0108.18101MR22 #12534
- [19] J. R. MUNKRES, Obstructions to imposing differentiable structures, Illinois J. Math., 8 (1964), 361-376. Zbl0126.18701MR31 #5209
- [20] M. NAGATA, Local rings, John Wiley, 1962. Zbl0123.03402MR27 #5790
- [21] R. PALAIS, Equivariant real algebraic differential topology, Part I. Smoothness categories and Nash manifolds, Notes Brandeis Univ., 1972. Zbl0281.57015
- [22] K. REICHARD, Nichtdifferenzierbare Morphismen differenzierbarer Räume, Manuscripta Math., 15 (1975), 243-250. Zbl0305.58003MR52 #6043
- [23] J. J. RISLER, Le théorème des zéros pour les idéaux de fonctions différentiables en dimension 2 et 3, Ann. Inst. Fourier, Grenoble, 26 (1976), 73-107. Zbl0324.46028MR54 #13108
- [24] M. SHIOTA, Differentiable functions equivalent to analytic functions, Publ. RIMS, Kyoto Univ., 9 (1973), 113-121. Zbl0271.58002MR49 #6272
- [25] M. SHIOTA, Transformations of germs of differentiable functions through changes of local coordinates, Publ. RIMS, Kyoto Univ., 9 (1973), 123-140. Zbl0271.58003MR51 #4307
- [26] M. SHIOTA, On germs of differentiable functions in two variables, Publ. RIMS, Kyoto Univ., 9 (1974), 319-324. Zbl0278.57013MR49 #6270
- [27] M. SHIOTA, Some results on formal power series and differentiable functions, Publ. RIMS, Kyoto Univ., 12 (1976), 49-53. Zbl0338.13026MR54 #3742
- [28] M. SHIOTA, Thesis, Univ. of Rennes, France, 1978.
- [29] L. C. SIEBENMANN, Deformation of homeomorphisms on stratified sets, Comm. Math. Helv, 47 (1972), 123-163. Zbl0252.57012MR47 #7752
- [30] H. SKODA, J. BRIANÇON, Sur la clôture intégrale d'un idéal de germes de fonctions holomorphes en un point de Cn, C.R. Acad. Sc. Paris, 278 (1974), 949-951. Zbl0307.32007MR49 #5394
- [31] J. C. TOUGERON, Idéaux de fonctions différentiables I, Ann. Inst. Fourier, 18 (1968), 177-240. Zbl0188.45102MR39 #2171
- [32] M. VAN DER PUT, Some properties of the ring of germs of C∞ functions, Compositio Math., 34 (1977), 99-108. Zbl0404.58012MR57 #1549
- [33] H. WHITNEY, A function not constant on a connected set of critical points, Duke Math. J., 1 (1935), 514-517. Zbl0013.05801JFM61.1117.01
- [34] H. WHITNEY, Local properties of analytic varieties, Differential and Combinatorial topology, Princeton Univ. Press, 1965, 205-244. Zbl0129.39402MR32 #5924
- [35] H. WHITNEY, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc., 36 (1934), 63-89. Zbl0008.24902MR1501735JFM60.0217.01
- [36] G. T. WHYBURN, Analytic topology, Amer. Math. Soc. Colloq. Publ., 28, 1942. Zbl0061.39301MR4,86b
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.