Abstract
A Fréchet vector space is a complete topological vector space the topology of which may be defined by a countable set of pseudo-norms. A Fréchet manifold M (modelled on E) is a space locally homeomorphic to a Fréchet vector space E (E is called the model of M). (No differentiability structure is imposed on M).
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References
J.W. Alexander, “On the subdivision of 3-space by a polyhedron”, Proc. Nat. Acad. Sc. U.S.A., t. 10, 1924, p. 6–8.
J. Cerf, “Topologie de certains espaces de plongements”, Bull. Soc. Math. France, t. 89, 1961, p. 226–380 (Thèse Sc. Math. Paris, 1960).
J. Cerf, “Sur les difféomorphismes de la sphère de dimension trois (Γ4 = 0)”, 1968, Lecture Notes in Math. # 53, Springer.
J. Cerf, “La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie”, Publications Mathématiques de l’I.H.E.S. n° 39 p. 5 à 173.
C.G. Gibson, K.W. Wirthmüller, A.A. du Plessis and E.J.N. Looijenga: Topological stability of smooth mappings, 1976, Lecture notes in Math. # 552, Springer.
Martin Golubitsky and Victor Guillemin: Stable mappings and their singularities, 1973, Graduate texts in Math. # 14, Springer.
Allen E. Hatcher: Homeomorphisms of sufficiently large P2-irreducible 3-manifolds, Topology 15 (1976), 343–347.
Allen E. Hatcher: Linearization in 3-dimensional topology, Proceedings of the International Congress of Mathematicians Helsinki, 1978, pp. 463–468.
Allen E. Hatcher: On the diffeomorphism group of S1 × S2, preprint.
David W. Henderson: Infinite dimensional manifolds are open subsets of Hilbert space, Topology Vol. 9, pp. 25–33.
Kervaire M. and Milnor, J.W.: Groups of homotopy spheres: I, Annals of Math. 77 (1963), 504–537.
N.H. Kuiper, Mathematical Review N° 6641 a-d, vol. 33, p. 1126 concerning J. Cerf “La nullité de πo (Diff S3)”.
François Laudenbach: Topologie de la dimension trois: homotopie et isotopie, Astérisque 12 (1974), Soc. Math, de France, 1974.
François Laudenbach et Oscar Zambrano: Disjonction à paramètres dans une variété de dimension 3, P2-irréductible, C.R. Acad. Sc. Paris, t. 288 (5 février 1979), Série A, 331–334.
John W. Milnor: On manifolds homeomorphic to the 7-spheres, Annals of Math. 64 (1956), 399–405.
John W. Milnor: Morse Theory, Annals of Mathematics Studies, Princeton University Press, #51.
John W. Milnor and James D. Stasheff: Characteristic classes, Annals of Mathematics Studies, Princeton University Press, # 76, 1974.
Bernard Morin et Jean-Pierre Petit: Problématique du retournement de la sphère, C.R. Acad. Sc. Paris, t. 287 (23 octobre 1978), Série A. 767–770.
Bernard Morin et Jean-Pierre Petit: Le retournement de la sphère, Pour la Science, n°15, janvier 1979, p. 34 à 49.
M. Morse and E. Baiada: Homotopy and homology related to the Schoenflies problem, Annals of Math. Series 2, t. 58, 1953, p. 142–165.
S.P. Novikov: Differentiable sphere bundles, Izv. Aka. Nauk, SSSR Mat 29 (1965), 1–96 (Am. Math. Soc. Translations, Ser. 2, Vol. 63).
Anthony Phillips: Turning a surface inside out, Scientific American, n° 214, pp. 112–120, May 1966.
Stephen Smale: A classification of immersions of the two-sphere, Trans. Amer. Math. Soc, 90, 1959, p. 281–290.
Stephen Smale: Diffeomorphisms of the 2-spheres, Proc. Amer. Math. Soc. 10 (1959), 621–626.
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© 1983 D. Reidel Publishing Company
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Chaltin, H. (1983). Embedded 2-Spheres in ℝ3 . In: Cahen, M., De Wilde, M., Lemaire, L., Vanhecke, L. (eds) Differential Geometry and Mathematical Physics. Mathematical Physics Studies, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7022-9_10
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DOI: https://doi.org/10.1007/978-94-009-7022-9_10
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