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

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.

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.

Shiota, Masahiro. Classification of Nash manifolds. Annales de l'Institut Fourier, Tome 33 (1983) no. 3, pp. 209-232. doi: 10.5802/aif.937
@article{AIF_1983__33_3_209_0,
     author = {Shiota, Masahiro},
     title = {Classification of {Nash} manifolds},
     journal = {Annales de l'Institut Fourier},
     pages = {209--232},
     year = {1983},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {33},
     number = {3},
     doi = {10.5802/aif.937},
     zbl = {0495.58001},
     mrnumber = {85b:58004},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.937/}
}
TY  - JOUR
AU  - Shiota, Masahiro
TI  - Classification of Nash manifolds
JO  - Annales de l'Institut Fourier
PY  - 1983
SP  - 209
EP  - 232
VL  - 33
IS  - 3
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.937/
DO  - 10.5802/aif.937
LA  - en
ID  - AIF_1983__33_3_209_0
ER  - 
%0 Journal Article
%A Shiota, Masahiro
%T Classification of Nash manifolds
%J Annales de l'Institut Fourier
%D 1983
%P 209-232
%V 33
%N 3
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.937/
%R 10.5802/aif.937
%G en
%F AIF_1983__33_3_209_0

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

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

[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. | Zbl | MR

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

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

[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. | Zbl | MR

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

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

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

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

Cité par Sources :