Classification of Nash manifolds
Shiota, Masahiro
Annales de l'Institut Fourier, Tome 33 (1983), p. 209-232 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

Une variété analytique semi-algébrique et une application analytique semi-algébrique sont appelées respectivement une variété de Nash et une application de Nash. Nous clarifions la catégorie des variétés de Nash et les applications de Nash.

A semi-algebraic analytic manifold and a semi-algebraic analytic map are called a Nash manifold and a Nash map respectively. We clarify the category of Nash manifolds and Nash maps.

@article{AIF_1983__33_3_209_0,
     author = {Shiota, Masahiro},
     title = {Classification of Nash manifolds},
     journal = {Annales de l'Institut Fourier},
     volume = {33},
     year = {1983},
     pages = {209-232},
     doi = {10.5802/aif.937},
     mrnumber = {85b:58004},
     zbl = {0495.58001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1983__33_3_209_0}
}

Shiota, Masahiro. Classification of Nash manifolds. Annales de l'Institut Fourier, Tome 33 (1983) pp. 209-232. doi : 10.5802/aif.937. http://gdmltest.u-ga.fr/item/AIF_1983__33_3_209_0/

[1] R. Benedetti, and A. Tognoli, On real algebraic vector bundles, Bull. Sc. Math., 104 (1980), 89-112. | MR 81e:14009 | Zbl 0421.58001

[2] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, I-II, Ann. Math., 79 (1964), 109-326. | MR 33 #7333 | Zbl 0122.38603

[3] S. Lojasiewicz, Ensemble semi-analytique, IHES, 1965.

[4] J.W. Milnor, Two complexes which are homeomorphic but combinatorially distinct, Ann. Math., 74 (1961), 575-590. | MR 24 #A2961 | Zbl 0102.38103

[5] J.W. Milnor, Lectures on the h-cobordism theorem, Princeton, Princeton Univ. Press, 1965. | MR 32 #8352 | Zbl 0161.20302

[6] T. Mostowski, Some properties of the ring of Nash functions, Ann. Scuola Norm. Sup. Pisa, III 2 (1976), 245-266. | Numdam | MR 54 #307 | Zbl 0335.14001

[7] R. Palais, Equivariant real algebraic differential topology, Part I, Smoothness categories and Nash manifolds, Notes Brandeis Univ., 1972. | Zbl 0281.57015

[8] J. J. Risler, Sur l'anneau des fonctions de Nash globales, C.R.A.S., Paris, 276 (1973), 1513-1516. | MR 47 #7057 | Zbl 0256.13014

[9] M. Shiota, On the unique factorization property of the ring of Nash functions, Publ. RIMS, Kyoto Univ., 17 (1981), 363-369. | MR 83a:58001 | Zbl 0503.58001

[10] M. Shiota, Equivalence of differentiable mappings and analytic mappings, Publ. Math. IHES, 54 (1981), 237-322. | Numdam | MR 84k:58039 | Zbl 0516.58012

[11] M. Shiota, Equivalence of differentiable functions, rational functions and polynomials, Ann. Inst. Fourier, 32, 4 (1982), 167-204. | Numdam | MR 84i:58023 | Zbl 0466.58006

[12] M. Shiota, Sur la factorialité de l'anneau des fonctions lisses rationnelles, C.R.A.S., Paris, 292 (1981), 67-70. | MR 82b:14009 | Zbl 0489.14013