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}, 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://www.numdam.org/articles/10.5802/aif.937/} }
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://www.numdam.org/articles/10.5802/aif.937/
[1] On real algebraic vector bundles, Bull. Sc. Math., 104 (1980), 89-112. | MR | Zbl
, and ,[2] Resolution of singularities of an algebraic variety over a field of characteristic zero, I-II, Ann. Math., 79 (1964), 109-326. | MR | Zbl
,[3] Ensemble semi-analytique, IHES, 1965.
,[4] Two complexes which are homeomorphic but combinatorially distinct, Ann. Math., 74 (1961), 575-590. | MR | Zbl
,[5] Lectures on the h-cobordism theorem, Princeton, Princeton Univ. Press, 1965. | MR | Zbl
,[6] Some properties of the ring of Nash functions, Ann. Scuola Norm. Sup. Pisa, III 2 (1976), 245-266. | Numdam | MR | Zbl
,[7] Equivariant real algebraic differential topology, Part I, Smoothness categories and Nash manifolds, Notes Brandeis Univ., 1972. | Zbl
,[8] Sur l'anneau des fonctions de Nash globales, C.R.A.S., Paris, 276 (1973), 1513-1516. | MR | Zbl
,[9] On the unique factorization property of the ring of Nash functions, Publ. RIMS, Kyoto Univ., 17 (1981), 363-369. | MR | Zbl
,[10] Equivalence of differentiable mappings and analytic mappings, Publ. Math. IHES, 54 (1981), 237-322. | Numdam | MR | Zbl
,[11] Equivalence of differentiable functions, rational functions and polynomials, Ann. Inst. Fourier, 32, 4 (1982), 167-204. | Numdam | MR | Zbl
,[12] Sur la factorialité de l'anneau des fonctions lisses rationnelles, C.R.A.S., Paris, 292 (1981), 67-70. | MR | Zbl
,Cité par Sources :