Immersioni aperte in dimensione infinita - Dipartimento di Matematica

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122 BIBLIOGRAFIA [De 85] K. Deimling, Nonlinear Functional Analysis. Springer, Berlin (1985). [Di 69] J. Dieudonné, Foundations of Modern Analysis. Academic Press, New York and London (1969). [DGZ 93] R. Deville, G. Godefroy, V. Zizler, Smoothness and renormings in Banach spaces. Pitman Monographs and Surveys in Pure and Applied Mathematics 64 (1993). [Dou 65] A. Douady, Un espace de Banach dont la groupe linéaire n’est pas connexe, Indag. Math. 68 (1965), 787–789. [Do 98] R.G. Douglas, Banach algebra techniques in operator theory. Springer, Berlin (1998). [Du 66] J. Dugundji, Topology. Allyn and Bacon, Inc. (1966). [Ee 67] J. Eells, Fredholm structures, in Proc. Symp. Non-linear Functional Analysis. Chicago (1967). [Ee-El 68] J. Eells, K.D. Elworthy, On the differential topology of Hilbertian manifolds. In Proc. Summer Institute on Global Analysis (1968). [Ee-El 70] J. Eells, K.D. Elworthy, Open embeddings of certain Banach manifolds. Ann. of Math. (2) 91 (1970), 465–485. [El 72] K.D. Elworthy, Embeddings, Isotopy and Stability of Banach manifolds, Compositio Mathematica (2) 24 (1972), 175–226. [El 70] K.D. Elworthy, Structure Fredholm sur les variétés banachiques. Analyse Globale, Sém. Math. Supérieures, Presses University of Montréal, Montreal (1970), 112–147. [El 68] K.D. Elworthy, Fredholm maps and GLc(E)-structures, Oxford Thesis (1967). Bull. Amer. Math. Soc. 74 (1968), 582–586. [El-Tr 68] K.D. Elworthy, A.J. Tromba, Fredholm maps and differential structures on Banach manifolds. In Proc. Summer Institute on Global Analysis (1968). [Fa 01] M. Fabian, Functional Analysis and Infinite-Dimensional Geometry. Springer, Berlin (2001). [Fo 99] G.F. Folland, Real Analysis. Interscience Wiley & Sons, Inc., New York (1999). [Go 58] R. Godement, Topologie Algébrique et Théorie des Faisceaux. Hermann 1958. [Gro 65] N. Grossman, Hilbert manifolds without epiconjugate points. Proc. Am. Math. Soc. 16 (1965), 1365–1371. [Gu 89] M. Gunther, On the perturbation problem associated to isometric embeddings of Riemannian manifolds. Ann. of Global Analysis and Geometry. 7 (1989), 69–77. [He 78] S. Helgason, Differential geometry, Lie groups and symmetric spaces. Academic Press New York (1978). [He 69] D.W. Henderson, Infinite-dimensional manifolds are open subsets of Hilbert space. Bull. AMS 75 (1969), 759–762. [He 70] D.W. Henderson, Infinite-dimensional manifolds are open subsets of Hilbert space. Topology 9 (1970), 25–34. [Hil 72] E. Hille, Methods in Classical and Functional Analysis. Addison-Wesley. Reading (1972). IMMERSIONI APERTE IN DIMENSIONE INFINITA
BIBLIOGRAFIA 123 [Hir 94] M. Hirsch, Differential Topology. Springer New Vork 1994. [Ion 73] A. Ionushauskas, On smooth partitions of unity on Hilbert manifolds, Lithuanian Mathematical Journal 13 (4) (1973), 595–601. [Jan 65] J. Jänich, Vektorraumbundel und der Raum der Fredholm–Operatoren, Math. Ann. 161 (1965), 129–142. [Ka 47] S. Kaplan, Homology properties of arbitrary subsets of euclidean spaces. Trans. Amer. Math. Soc. 62 (1947), 248–271. [Ka 80] T. Kato, Perturbation theory for linear operators. Springer Berlin 1980. [Kel 55] J.L. Kelley, General Topology. Springer, Berlin (1955). [KG 83] A.A. Kirillov, A.D. Gviˇsiani, Teoremi e problemi dell’analisi funzionale. Mir Mosca 1983. [Kl 53] V.L. Klee, Convex bodies and periodic homeomorphisms in Hilbert space. Trans. Amer. Math. Soc., 74 (1953), 10–43. [Kl 82] W. Klingenberg, Riemannian geometry. De Gruyter studies in Mathemathics. New York 1982. [Ko-No 63] S. Kobayashi, K. Nomizu, Foundations of differential geometry, I. Interscience Wiley & Sons, Inc., New York (1963). [Ku 65] N.H. Kuiper, The homotopy type of the unitary group of Hilbert spaces. Topology 3 (1965), 19–30. [Ku-Bu 69] N.H. Kuiper, D. Burghelea, Hilbert manifolds. Ann. of Math. 90 (1969), 379–417. [Lan 01] S. Lang, Fundamentals of Differential Geometry. Springer New York (2001). [Lan 83] S. Lang, Real Analysis. Addison-Wesley publishing company (1983). [Lo 63] E.R. Lorch, D. Laugwitz, Riemannian metrics associated with convex bodies in normed spaces. Am. J. Math. 78, (4) (1956), 889–894. [McL 98] S. Mac Lane, Categories for the Working Mathematician. Springer New York (1998). [Mi 61] J. Milnor, Differentiable structures. Notes at Princeton Univ. (1961). [Mi 63] J. Milnor, Morse Theory. Ann. Math. Studies 53, Princeton University Press (1963). [Mi 68] J. Milnor, Topology from the differential viewpoint. The University Press of Virginia Charlottesville (1968). [Mo 68] N. Moulis, Sur les variétés Hilbertiennes et les fonctions non dégénerées, Indag. Math. 30 (1968), 497-511. [Mo 70] N. Moulis, Stability of Hilberts manifolds, Global Analysis Proc. Sympos. Pure Math. 15 (1970), 157-165. [Mu 68] K.K. Mukherjea, Fredholm structures and cohomology. Cornell Thesis (1968). Bull Amer. Math. Soc. 74 (1968), 493-496. [Mu 70] K.K. Mukherjea, The homotopy theory of Fredholm manifolds. Transactions of the American Mathematical Society 149 (1970), 653-663. 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
Page 83 and 84: C.1 Varietà di dimensione infinita
Page 85 and 86: C.1 Varietà di dimensione infinita
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: Bibliografia [Abr 62] R. Abraham, L
Page 137: BIBLIOGRAFIA 125 [Wa 60] C.T.C. Wal
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