Embeddings, isotopy and stability of Banach manifolds
Elworthy, K. D.
Compositio Mathematica, Tome 25 (1972), p. 175-226 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1972-01-01
@article{CM_1972__24_2_175_0,
     author = {Elworthy, Kenneth David},
     title = {Embeddings, isotopy and stability of Banach manifolds},
     journal = {Compositio Mathematica},
     volume = {25},
     year = {1972},
     pages = {175-226},
     mrnumber = {305433},
     zbl = {0228.58001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1972__24_2_175_0}
}

Elworthy, K. D. Embeddings, isotopy and stability of Banach manifolds. Compositio Mathematica, Tome 25 (1972) pp. 175-226. http://gdmltest.u-ga.fr/item/CM_1972__24_2_175_0/

R.D. Anderson [1] Homeomorphisms of infinite dimensional manifolds, I.C.M. Nice 1970. | MR 454983 | Zbl 0228.57007

R.D. Anderson [1a] Proper homotopies in l2 manifolds, Comp. Mat. 23(1971) 155-157. | Numdam | MR 290411 | Zbl 0218.57007

R.D. Anderson AND J.D. Mccharen [2] On extending homeomorphisms to Fréchet manifolds, Proc. A.M.S. 25 (1970) 283-289. | MR 258064 | Zbl 0203.25805

R. Bonic AND J. Frampton [3] Smooth functions on Banach manifolds, J. of Math. and Mech. 15 (1966) 877-898. | MR 198492 | Zbl 0143.35202

R. Bonic, J. Frampton AND A.J. Tromba [4] ∧-manifolds, Journal of Functional Analysis 3 (1969). | Zbl 0179.17602

D. Burghelea [5] (i) Imbedding Hilbert manifolds in finite co-dimension, Séminaire de mathématiques supérieures, Montréal, 1969.

(ii) Imbedding Hilbert manifolds with given normal bundle, Math. Ann. 187 (1970) 207-219. | MR 266253 | Zbl 0184.27104

D. Burghelea [6] Diffeomorphisms for Hilbert manifolds and handle decompositions, Bulletin A.M.S. 76 (1970) 352-357. | MR 258065 | Zbl 0197.20603

D. Burghelea AND N.H. Kuiper [7] Hilbert manifolds, Ann. of Math. 90 (1969) 379-417. | MR 253374 | Zbl 0195.53501

M. Day [8] Normed linear spaces, Ergebn. Math. Heft 21 (1958). | MR 94675 | Zbl 0082.10603

M. Day [8a] On the basis problem in Banach spaces, Proc. A.M.S. 13 (1962) 655-658. | MR 137987 | Zbl 0109.33601

A. Douady [9] Le problème des modules pour les sous-espaces analytiques compacts d'un espace analytique donné, Ann. Inst. Fourier, Grenoble 16 (1966) 1-95. | Numdam | MR 203082 | Zbl 0146.31103

A. Douady [10] Un espace de Banach dont le groupe linéare n'est pas connexe, Nederl. Akad.v. W. A68 = Ind. Math. 27 (1965) 787-789. | MR 187056 | Zbl 0178.26403

I Edelstein, B. MitjaginAND E. Semenov [11] The Linear groups of C and L 1 are contractible, Bull. Acad. Pol. Sc. Ser. Math., 18 No. 1, 27-33 (1970). | MR 341524 | Zbl 0192.47401

J. Eells [12] A setting for global analysis, Bull. A.M.S. 72 (1966) 751-807. | MR 203742 | Zbl 0191.44101

J. Eells AND K.D. Elworthy [13] (OECBM) Open embeddings of certain Banach manifolds, Ann. of Math. 91 (1970) 465-485. | MR 263120 | Zbl 0198.28804

J. Eells AND N.H. Kuiper [14] Homotopy negligible subsets, Comp. Math. 21 (1969) 155-161. | Numdam | MR 253331 | Zbl 0181.51401

K.D. Elworthy [15] Fredholm maps and GLc(E) structures, Bull A.M.S. 74 (1968) 582-586. | MR 224113 | Zbl 0159.25102

K.D. Elworthy AND A.J. Tromba [16] Fredholm maps and differential structures on Banach manifolds. Global Analysis (Proc. Sympos. Pure Math., Vol. XV, Berkeley, Calif., 1968) 45-94 A.M.S. (1970). | MR 264708 | Zbl 0206.52504

R. Herman AND R. Whitley [17] An example concerning reflexivity, Studia Math. 28 (1967) 289-294. | MR 215056 | Zbl 0148.37101

M. Hirsch [18] On tangential equivalence of manifolds. Ann. of Math. 83 (1966) 211-217. | MR 205265 | Zbl 0137.17704

R.C. James [19] Bases and reflexivity of Banach spaces, Ann. of Math. 52 (1950) 518-527. | MR 39915 | Zbl 0039.12202

N.H. Kuiper [20] Les variétés hilbertiens, Séminaire de Mathématiques Supérieures, Conférence Montréal 1969. | Zbl 0216.45704

N.H. Kuiper [21] The differential topology of separable Banach manifolds, ICM Nice 1970. | MR 455010 | Zbl 0223.58002

N.H. Kuiper AND Besseline Terpstra [22] Differentiable closed embeddings of Banach manifolds, Conference in honour of G. de Rham, Springer Verlag (1970) 118-125. | MR 264709 | Zbl 0193.24001

S. Lang [23] Introduction to differentiable manifolds, Interscience, New York 1962. | MR 155257 | Zbl 0103.15101

E. Michael [24] Continuous selections I, Ann. of Math. 63 (1956) 361-382. | MR 77107 | Zbl 0071.15902

J. Milnor [25] Der Ring der Vektorraumbündel eines topologischen Raumes, Bonn 1959 (lecture notes).

B.S. Mitjagin [26] Contractibility of the Linear group of a function Banach space, Uspechi Mat. Nauk 26 (1970).

B.S. Mitjagin AND I.S. Edelstein [27] The homotopy type of the linear groups of two classes of Banach spaces, Functional Analysis 4 (1970). | MR 341526 | Zbl 0228.47030

Nicole Moulis [28] Sur les variétés hilbertiennes et les fonctions non dégénérées, Nederl. Akad.v. W. A71 = Ind. Math. 30 (1968) 497-511. | MR 254876 | Zbl 0167.50204

Nicole Moulis [29] Approximation de fonctions différentiables sur certains espaces de Banach. Thèse, Paris, 1970 (to appear). | Numdam | Zbl 0271.41025

Nicole Moulis [30] Structure Fredholm sur les variétés Banachiques, Notes of lectures by K. D. Elworthy. Séminaire de mathématiques supérieures, Montréal, 1969.

G. Neubauer [31 ] On a class of sequence spaces with contractible linear group (Mimeographed notes Berkeley 1967).

R.S. Palais [32] Homotopy theory of infinite dimensional manifolds, Topology 5 (1966) 1-16. | MR 189028 | Zbl 0138.18302

A. Pelczynski [33] Projections in certain Banach spaces, Studia Math. 19 (1960) 209-228. | MR 126145 | Zbl 0104.08503

D. Przeworska-Rolewicz AND S. Rolewicz [34] Equations in linear spaces, Monografie Matematyczne 47, PWN, Warsaw 1968. | Zbl 0181.40501

Karen Uhlenbeck [35] Integrals with non-degenerate critical points, Bull. A.M.S. 76 (1970) 125-128. | MR 254873 | Zbl 0198.43403

J. Wells [36] Differentiable functions on c0, Bull. A.M.S. 75 (1969) 117-118. | MR 234273 | Zbl 0187.07402

J. Wells [36a] C1 partitions of unity on non-separable Hilbert space, Bull. A.M.S. 77 (1971) 804-807. | MR 279839 | Zbl 0226.58005

J.L. Kelley [37] General Topology, Van Nostrand 1955. | MR 70144 | Zbl 0066.16604