Embeddings, isotopy and stability of Banach manifolds

K. D. Elworthy

Compositio Mathematica (1972)

  • Volume: 24, Issue: 2, page 175-226
  • ISSN: 0010-437X

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Elworthy, K. D.. "Embeddings, isotopy and stability of Banach manifolds." Compositio Mathematica 24.2 (1972): 175-226. <http://eudml.org/doc/89117>.

@article{Elworthy1972,
author = {Elworthy, K. D.},
journal = {Compositio Mathematica},
language = {eng},
number = {2},
pages = {175-226},
publisher = {Wolters-Noordhoff Publishing},
title = {Embeddings, isotopy and stability of Banach manifolds},
url = {http://eudml.org/doc/89117},
volume = {24},
year = {1972},
}

TY - JOUR
AU - Elworthy, K. D.
TI - Embeddings, isotopy and stability of Banach manifolds
JO - Compositio Mathematica
PY - 1972
PB - Wolters-Noordhoff Publishing
VL - 24
IS - 2
SP - 175
EP - 226
LA - eng
UR - http://eudml.org/doc/89117
ER -

References

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  1. R.D. Anderson [1] Homeomorphisms of infinite dimensional manifolds, I.C.M.Nice1970. Zbl0228.57007MR454983
  2. R.D. Anderson [1a] Proper homotopies in l2 manifolds, Comp. Mat.23(1971) 155-157. Zbl0218.57007MR290411
  3. R.D. Anderson AND J.D. Mccharen [2] On extending homeomorphisms to Fréchet manifolds, Proc. A.M.S.25 (1970) 283-289. Zbl0203.25805MR258064
  4. R. Bonic AND J. Frampton [3] Smooth functions on Banach manifolds, J. of Math. and Mech.15 (1966) 877-898. Zbl0143.35202MR198492
  5. R. Bonic, J. Frampton AND A.J. Tromba [4] ∧-manifolds, Journal of Functional Analysis3 (1969). Zbl0179.17602
  6. D. Burghelea [5] (i) Imbedding Hilbert manifolds in finite co-dimension, Séminaire de mathématiques supérieures, Montréal, 1969. 
  7. (ii) Imbedding Hilbert manifolds with given normal bundle, Math. Ann.187 (1970) 207-219. Zbl0184.27104MR266253
  8. D. Burghelea [6] Diffeomorphisms for Hilbert manifolds and handle decompositions, Bulletin A.M.S.76 (1970) 352-357. Zbl0197.20603MR258065
  9. D. Burghelea AND N.H. Kuiper [7] Hilbert manifolds, Ann. of Math.90 (1969) 379-417. Zbl0195.53501MR253374
  10. M. Day [8] Normed linear spaces, Ergebn. Math. Heft 21 (1958). Zbl0082.10603MR94675
  11. M. Day [8a] On the basis problem in Banach spaces, Proc. A.M.S. 13 (1962) 655-658. Zbl0109.33601MR137987
  12. A. Douady [9] Le problème des modules pour les sous-espaces analytiques compacts d'un espace analytique donné, Ann. Inst. Fourier, Grenoble16 (1966) 1-95. Zbl0146.31103MR203082
  13. 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. Zbl0178.26403MR187056
  14. 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). Zbl0192.47401MR341524
  15. J. Eells [12] A setting for global analysis, Bull. A.M.S. 72 (1966) 751-807. Zbl0191.44101MR203742
  16. J. Eells AND K.D. Elworthy [13] (OECBM) Open embeddings of certain Banach manifolds, Ann. of Math.91 (1970) 465-485. Zbl0198.28804MR263120
  17. J. Eells AND N.H. Kuiper [14] Homotopy negligible subsets, Comp. Math.21 (1969) 155-161. Zbl0181.51401MR253331
  18. K.D. Elworthy [15] Fredholm maps and GLc(E) structures, Bull A.M.S.74 (1968) 582-586. Zbl0159.25102MR224113
  19. 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) 45-94A.M.S. (1970). Zbl0206.52504MR264708
  20. R. Herman AND R. Whitley [17] An example concerning reflexivity, Studia Math.28 (1967) 289-294. Zbl0148.37101MR215056
  21. M. Hirsch [18] On tangential equivalence of manifolds. Ann. of Math.83 (1966) 211-217. Zbl0137.17704MR205265
  22. R.C. James [19] Bases and reflexivity of Banach spaces, Ann. of Math.52 (1950) 518-527. Zbl0039.12202MR39915
  23. N.H. Kuiper [20] Les variétés hilbertiens, Séminaire de Mathématiques Supérieures, Conférence Montréal1969. Zbl0216.45704
  24. N.H. Kuiper [21] The differential topology of separable Banach manifolds, ICMNice1970. Zbl0223.58002MR455010
  25. 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. Zbl0193.24001MR264709
  26. S. Lang [23] Introduction to differentiable manifolds, Interscience, New York1962. Zbl0103.15101MR155257
  27. E. Michael [24] Continuous selections I, Ann. of Math.63 (1956) 361-382. Zbl0071.15902MR77107
  28. J. Milnor [25] Der Ring der Vektorraumbündel eines topologischen Raumes, Bonn1959 (lecture notes). 
  29. B.S. Mitjagin [26] Contractibility of the Linear group of a function Banach space, Uspechi Mat. Nauk26 (1970). 
  30. B.S. Mitjagin AND I.S. Edelstein [27] The homotopy type of the linear groups of two classes of Banach spaces, Functional Analysis4 (1970). Zbl0228.47030MR341526
  31. Nicole Moulis [28] Sur les variétés hilbertiennes et les fonctions non dégénérées, Nederl. Akad.v. W. A71 = Ind. Math. 30 (1968) 497-511. Zbl0167.50204MR254876
  32. Nicole Moulis [29] Approximation de fonctions différentiables sur certains espaces de Banach. Thèse, Paris, 1970 (to appear). Zbl0271.41025
  33. Nicole Moulis [30] Structure Fredholm sur les variétés Banachiques, Notes of lectures by K. D. Elworthy. Séminaire de mathématiques supérieures, Montréal, 1969. 
  34. G. Neubauer [31 ] On a class of sequence spaces with contractible linear group (Mimeographed notes Berkeley1967). 
  35. R.S. Palais [32] Homotopy theory of infinite dimensional manifolds, Topology5 (1966) 1-16. Zbl0138.18302MR189028
  36. A. Pelczynski [33] Projections in certain Banach spaces, Studia Math.19 (1960) 209-228. Zbl0104.08503MR126145
  37. D. Przeworska-Rolewicz AND S. Rolewicz [34] Equations in linear spaces, Monografie Matematyczne47, PWN, Warsaw1968. Zbl0181.40501
  38. Karen Uhlenbeck [35] Integrals with non-degenerate critical points, Bull. A.M.S.76 (1970) 125-128. Zbl0198.43403MR254873
  39. J. Wells [36] Differentiable functions on c0, Bull. A.M.S. 75 (1969) 117-118. Zbl0187.07402MR234273
  40. J. Wells [36a] C1 partitions of unity on non-separable Hilbert space, Bull. A.M.S. 77 (1971) 804-807. Zbl0226.58005MR279839
  41. J.L. Kelley [37] General Topology, Van Nostrand1955. Zbl0066.16604MR70144

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