no. 3
Classification of Nash manifolds
Annales de l'Institut Fourier, Tome 33 (1983) no. 3, pp. 209-232.

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.

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     author = {Shiota, Masahiro},
     title = {Classification of {Nash} manifolds},
     journal = {Annales de l'Institut Fourier},
     pages = {209--232},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {33},
     number = {3},
     year = {1983},
     doi = {10.5802/aif.937},
     mrnumber = {85b:58004},
     zbl = {0495.58001},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.937/}
}
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Shiota, Masahiro. Classification of Nash manifolds. Annales de l'Institut Fourier, Tome 33 (1983) no. 3, pp. 209-232. doi : 10.5802/aif.937. http://archive.numdam.org/articles/10.5802/aif.937/

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

[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 | Zbl

[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 | Zbl

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

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

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

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

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

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

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

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

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