Immersioni aperte in dimensione infinita - Dipartimento di Matematica

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124 BIBLIOGRAFIA [Mu 71] K.K. Mukherjea, The algebraic topology of Fredholm manifolds. Analyse Globale, Sém. Math. Supérieures 42 Presses University of Montréal, Montreal (1971), 163-177. [Mun 00] J. Munkres, Topology. 2nd edition, Prentice Hall, (2000). [Na 56] J.F. Nash, The imbedding problem for Riemannian manifolds. Ann. of Math. 63 (1956), 20–63. [Neu 67] G. Neubauer, On a class of sequence spaces with contractible linear group, Notes, University of California, Berkeley, Calif. (1967). [Nom 61] K. Nomizu, H. Ozeki, The Existence of Complete Riemannian Metrics. Proc. Am. Math. Soc. 12 (1961), 889–891. [Os 82] H. Osborne, Vector Bundles, Volume I. Academic Press London 1982. [PA 73] G. Prodi, A. Ambrosetti, Analisi Non Lineare, I quaderno. Pisa (1973). [Pa 63] R. Palais, On the homotopy of a certain class of Banach algebras. Notes at Brandeis University (Mimeographed). (1963). [Pa 66] R. Palais, Homotopy theory of infinite dimensional manifolds. Topology 5 (1966), 1-16. [PW 51] R. Putnam, A. Winter, The connectedness of the orthogonal group in Hilbert space, Proc. Nat. Acad. Sci., Wash. 37 (1951), 110–112. [PW 52] R. Putnam, A. Winter, The orthogonal group in Hilbert space, Am. J. Math. 74 (1952), 52–78. [Ri 55] F. Riesz, B. Sz.-Nagy Functional Analysis. Ungar Publishing Co., New York, (1955). [Ro 94] J.M. Roig, E.O. Domínguez, Embedding of Hilbert Manifolds with smooth boundary into semispaces of Hilbert spaces. The author provides an electronic version of the manuscript at http://citeseer.ist.psu.edu/roig. [Sm 58] S. Smale, A classification of immersions of the two-sphere. Trans. Amer. Math. Soc. 90 (1958), 281–290. MR 0104227 (21:2984). [Sm 59] S. Smale, The classification of immersions of spheres in Euclidean spaces. Ann. of Math. 69 (1959), 27–34. MR 0105117 (21:3862). [Sm 65] S. Smale, An Infinite Dimensional Version of Sard’s Theorem. American Journal of Mathematics (4) 87 (1970), 861–866. [Sol 98] R.M. Solovay, About the last part of Nash’s proof for “The Imbedding Problem for Riemannian Manifolds”. There is an electronic version of the manuscript at http://www.math.princeton.edu. [Sp 79] M. Spivak, A Comprehensive Introduction to Differential Geometry: Volume II. Publish or Perish, Inc. (1979). [St 65] N. Steenrod, The Topology of Fibre Bundles. Princeton University Press. Princeton 1965. [Th 57] R. Thom, La classification des immersions. Sém. Bourbaki (1957/58), Exp. 157. [Tor 73] H. Toruńczyk, Smooth partitions of unity on some non-separable Banach spaces. Studia Math. 46 (1973), 43-51. There is an electronic version of the manuscript at http://matwbn.icm.edu.pl. IMMERSIONI APERTE IN DIMENSIONE INFINITA
BIBLIOGRAFIA 125 [Wa 60] C.T.C. Wall, Differential topology. Notes at Cambridge Univ. (1960/61). [Wa 87] F. Warner, Foundations of Differentiable Manifolds and Lie Groups. Springer New York (1987). [Ze 86] E. Zeidler, Nonlinear functional analysis and its applications I. Fixed-point theorems. Springer New York-Berlin (1986). RAUL TOZZI
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Università degli Studi di Pisa Fac
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Prefazione L’obiettivo principale
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S 1 , che certamente non ammette un
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Notazioni Notazioni di uso corrente
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xii INDICE C.2.2 Fibrati Hilbertian
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2 Fenomeni della dimensione infinit
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10 Fenomeni della dimensione infini
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Capitolo 2 Embedding aperti di vari
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2.1 Introduzione 21 (v) se F = {O}
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2.1 Introduzione 23 applicazione ξ
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2.2 Mappe di Fredholm di indice zer
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2.3 Filtrazioni di Fredholm 33 Nell
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2.4 Filtrazioni di Fredholm totalme
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2.4 Filtrazioni di Fredholm totalme
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2.5 Filtrazioni di Fredholm augment
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2.6 Raffinamento delle tecniche lay
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2.6 Raffinamento delle tecniche lay
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2.7 Prova del teorema di embedding
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Appendice A Propedeuticità topolog
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A.2 Assiomi di numerabilità 63 Lem
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A.3 La categoria di Baire 65 • X
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Appendice B Mappe di Fredholm: teor
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Appendice C Geometria differenziale
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C.1 Varietà di dimensione infinita
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Page 87 and 88: C.2 Fibrati vettoriali 75 FV 3. Per
Page 89 and 90: C.2 Fibrati vettoriali 77 definita
Page 91 and 92: C.3 Partizioni dell’unità 79 Chi
Page 93 and 94: C.4 Varietà Riemanniane 81 Sia τ
Page 95: C.4 Varietà Riemanniane 83 Controe
Page 98 and 99: 86 Intorni tubolari una sezione di
Page 100 and 101: 88 Intorni tubolari Dimostrazione.
Page 102 and 103: 90 Intorni tubolari Allora esiste u
Page 104 and 105: 92 Intorni tubolari di h(X). Infine
Page 106 and 107: 94 Intorni tubolari D.6 Costruzione
Page 108 and 109: 96 Intorni tubolari Notazione 1. In
Page 110 and 111: 98 Intorni tubolari Osservazione D.
Page 112 and 113: 100 Mappe di Fredholm: teoria non l
Page 118 and 119: 106 Spray Si osservi che la composi
Page 120 and 121: 108 Spray È immediato verificare d
Page 122 and 123: 110 Spray Calcoliamo (T h) ′ (x,
Page 125 and 126: Appendice G Analisi funzionale line
Page 127 and 128: G.1 Richiami di analisi lineare neg
Page 129 and 130: G.2 Richiami di analisi lineare neg
Page 131 and 132: G.3 Piega in dimensione infinita 11
Page 133 and 134: Bibliografia [Abr 62] R. Abraham, L
Page 135: BIBLIOGRAFIA 123 [Hir 94] M. Hirsch
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Immersioni aperte in dimensione infinita - Dipartimento di Matematica

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