Classification of Nash manifolds

Masahiro Shiota

Annales de l'institut Fourier (1983)

  • Volume: 33, Issue: 3, page 209-232
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Shiota, Masahiro. "Classification of Nash manifolds." Annales de l'institut Fourier 33.3 (1983): 209-232. <http://eudml.org/doc/74597>.

@article{Shiota1983,
abstract = {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.},
author = {Shiota, Masahiro},
journal = {Annales de l'institut Fourier},
keywords = {Nash manifolds; semi-algebraic analytic manifold; Euclidean space; Nash map; Nash diffeomorphic},
language = {eng},
number = {3},
pages = {209-232},
publisher = {Association des Annales de l'Institut Fourier},
title = {Classification of Nash manifolds},
url = {http://eudml.org/doc/74597},
volume = {33},
year = {1983},
}

TY - JOUR
AU - Shiota, Masahiro
TI - Classification of Nash manifolds
JO - Annales de l'institut Fourier
PY - 1983
PB - Association des Annales de l'Institut Fourier
VL - 33
IS - 3
SP - 209
EP - 232
AB - 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.
LA - eng
KW - Nash manifolds; semi-algebraic analytic manifold; Euclidean space; Nash map; Nash diffeomorphic
UR - http://eudml.org/doc/74597
ER -

References

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  2. [2] H. HIRONAKA, Resolution of singularities of an algebraic variety over a field of characteristic zero, I-II, Ann. Math., 79 (1964), 109-326. Zbl0122.38603MR33 #7333
  3. [3] S. LOJASIEWICZ, Ensemble semi-analytique, IHES, 1965. 
  4. [4] J.W. MILNOR, Two complexes which are homeomorphic but combinatorially distinct, Ann. Math., 74 (1961), 575-590. Zbl0102.38103MR24 #A2961
  5. [5] J.W. MILNOR, Lectures on the h-cobordism theorem, Princeton, Princeton Univ. Press, 1965. Zbl0161.20302MR32 #8352
  6. [6] T. MOSTOWSKI, Some properties of the ring of Nash functions, Ann. Scuola Norm. Sup. Pisa, III 2 (1976), 245-266. Zbl0335.14001MR54 #307
  7. [7] R. PALAIS, Equivariant real algebraic differential topology, Part I, Smoothness categories and Nash manifolds, Notes Brandeis Univ., 1972. Zbl0281.57015
  8. [8] J. J. RISLER, Sur l'anneau des fonctions de Nash globales, C.R.A.S., Paris, 276 (1973), 1513-1516. Zbl0256.13014MR47 #7057
  9. [9] M. SHIOTA, On the unique factorization property of the ring of Nash functions, Publ. RIMS, Kyoto Univ., 17 (1981), 363-369. Zbl0503.58001MR83a:58001
  10. [10] M. SHIOTA, Equivalence of differentiable mappings and analytic mappings, Publ. Math. IHES, 54 (1981), 237-322. Zbl0516.58012MR84k:58039
  11. [11] M. SHIOTA, Equivalence of differentiable functions, rational functions and polynomials, Ann. Inst. Fourier, 32, 4 (1982), 167-204. Zbl0466.58006MR84i:58023
  12. [12] M. SHIOTA, Sur la factorialité de l'anneau des fonctions lisses rationnelles, C.R.A.S., Paris, 292 (1981), 67-70. Zbl0489.14013MR82b:14009

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