Les voisinages ouverts réguliers : critères homotopiques d'existence

L. Siebenmann; L. Guillou; H. Hähl

Annales scientifiques de l'École Normale Supérieure (1974)

  • Volume: 7, Issue: 3, page 431-461
  • ISSN: 0012-9593

How to cite


Siebenmann, L., Guillou, L., and Hähl, H.. "Les voisinages ouverts réguliers : critères homotopiques d'existence." Annales scientifiques de l'École Normale Supérieure 7.3 (1974): 431-461. <http://eudml.org/doc/81944>.

author = {Siebenmann, L., Guillou, L., Hähl, H.},
journal = {Annales scientifiques de l'École Normale Supérieure},
language = {fre},
number = {3},
pages = {431-461},
publisher = {Elsevier},
title = {Les voisinages ouverts réguliers : critères homotopiques d'existence},
url = {http://eudml.org/doc/81944},
volume = {7},
year = {1974},

AU - Siebenmann, L.
AU - Guillou, L.
AU - Hähl, H.
TI - Les voisinages ouverts réguliers : critères homotopiques d'existence
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1974
PB - Elsevier
VL - 7
IS - 3
SP - 431
EP - 461
LA - fre
UR - http://eudml.org/doc/81944
ER -


  1. [A] R. D. ANDERSON, Topological properties of the Hilbert cube and the infinite product of open intervals (Trans. Amer. Math. Soc., vol. 126, 1967, p. 200-216). Zbl0152.12601MR34 #5045
  2. [AB] R. D. ANDERSON et R. H. BING, A complete elementary proof that Hilbert space is homeomorphic to the countable infinite product of lines (Bull. Amer. Math. Soc., vol. 74, 1968, p. 771-792). Zbl0189.12402MR37 #5847
  3. [AC] R. D. ANDERSON et J. D. MC CHAREN, On extending homeomorphisms to Frechet manifolds (Proc. Amer. Math. Soc., vol. 25, 1970, p. 283-289). Zbl0203.25805MR41 #2711
  4. [Bo1] K. BORSUK, Theory of Retracts, PWN, Warszawa, 1967. Zbl0153.52905MR35 #7306
  5. [Bo2] K. BORSUK, Theory of shape, Aarhus Univ. (Lecture notes Séries, n° 28, 1971). Zbl0232.55021MR45 #2679
  6. [Br] J. L. BRYANT, Approximating embedding of polyhedra in codimension three (Trans. Amer. Math. Soc., vol. 170, 1972, p. 85-95). Zbl0259.57007MR46 #6365
  7. [B-S] J. L. BRYANT et C. L. SEEBECK III, Locally nice embeddings in codimension three (Quart. J. Math., Oxford, vol. 21, 1970, p. 265-272). Zbl0199.26703MR44 #7560
  8. [Ch1] T. CHAPMAN, Compact Hilbert cube manifolds and the invariance of Whitehead torsion (Bull. Amer. Math. Soc., vol. 79, 1973, p. 52-56). Zbl0251.57004MR49 #11518
  9. [Ch2] T. A. CHAPMAN, Notices Amer. Math. Soc., vol. 19, 1972, p. A-810. 
  10. [Ch3] T. CHAPMAN, Notes on Hilbert cube manifolds (miméo.) Univ. of Kentucky at Lexington, 1973. 
  11. [Co] M. M. COHEN, A general theory of relative regular neighborhoods (Trans. Amer. Math. Soc., vol. 136, 1969, p. 189-229). Zbl0182.57602MR40 #2052
  12. [Do] A. DOLD, Lectures on algebraic topology, Springer-Verlag, Berlin-Heidelberg-New-York, 1972. Zbl0234.55001MR54 #3685
  13. [E] R. D. EDWARDS, Topological general position, preprint UCLA 1974. 
  14. [EW] S. EILENBERG et R. L. WILDER, Uniform local connectedness and contractibility (Amer. J. Math., vol. 64, 1942, p. 613-622). Zbl0061.41103MR4,87e
  15. [F] F. T. FARRELL, The obstruction to fibering a manifold over a circle [Actes. Cong. Ind. Math., 1970 (Nice), tome 2, p. 69-72, Gauthier-Villars, 1971]. Zbl0231.57019
  16. [FA] R. H. FOX et E. ARTIN, Some wild cells and spheres in three dimensional space (Ann. of Math., (2), vol. 49, 1948, p. 979-990). Zbl0033.13602MR10,317g
  17. [F] R. H. FOX, On shape (Fund. Math., vol. 74, 1972, p. 47-71). Zbl0232.55023MR45 #5973
  18. [GH] L. GUILLOU et H. HÄHL, Les voisinages réguliers ouverts : critères homotopiques d'identification (à paraître). Zbl0344.57002
  19. [He] D. W. HENDERSON, Infinite-dimentional manifolds are open subsets of Hilbert space (Topology, vol. 9, 1970, p. 25-33). Zbl0167.51904MR40 #3581
  20. [Hd] J. F. P. HUDSON, Piecewise-linear, Topology, W. A. Benjamin Inc., New-York et Amsterdam, 1969. Zbl0189.54507MR40 #2094
  21. [HP] L. S. HUSH et T. M. PRICE, Finding a boundary for a 3-manifold (Ann. of Math., (2), vol. 91, 1970, p. 223-235 et (2), vol. 93, 1971, p. 486-488). Zbl0169.55302
  22. [J] F. E. A. JOHNSON, Lefschetz duality and topological neighbourhoods (Trans. Amer. Math. Soc., vol. 172, 1972, p. 95-110). Zbl0264.57004MR46 #9990
  23. [KS1] R. C. KIRBY et L. C. SIEBENMANN, Deformation of smooth and piecewise linear manifold structures II, Sliced families (preprint). 
  24. [KS2] R. C. KIRBY et L. C. SIEBENMANN, Some basic theorems about topological manifolds (preprint). 
  25. [Mc1] D. R. MC MILLAN Jr., UV-properties and related topics, Notes of B. J. SMITH (mimeographed) Florida State Univ., 1970. 
  26. [Mc2] D. R. MC MILLAN Jr., A criterion for cellularity in a manifold II (Trans. Amer. Math. Soc., vol. 126, 1967, p. 217-224). Zbl0155.31603MR34 #8392
  27. [Mil] R. T. MILLER, Approximating codimension 3 embeddings (Ann. of Math., vol. 95, 1972, p. 406-416). Zbl0208.51801MR46 #6366
  28. [Mi1] J. W. MILNOR, On spaces having the homotopy type of CW-complex (Trans. Amer. Math. Soc., vol. 90, 1959, p. 272-280). Zbl0084.39002MR20 #6700
  29. [Mi2] J. W. MILNOR, Characteristic classes Notes, Appendix A, Princeton, Mars 1964. 
  30. [Sp] E. H. SPANIER, Algebraic Topology, Mc Graw-Hill, 1966. Zbl0145.43303MR35 #1007
  31. [S1] L. C. SIEBENMANN, The obstruction to finding a boundary for an open manifold of dimension &gt; 5 (Thesis, Princeton 1965, Univ. Microfilms, Order n° 66-5012, Box 1346 Ann. Arbor, Michigan). 
  32. [S2] L. C. SIEBENMANN, Version de [S1] (à paraître). 
  33. [S3] L. C. SIEBENMANN, Open regular neighborhoods of compacta (Notices Amer. Math. Soc., vol. 14, 1967, n° 67 T-26, p. 135). 
  34. [S4] L. C. SIEBENMANN, The structure of tame ends (Notices Amer. Math. Soc., vol. 13, 1966, n° 66 T-531, p. 862). 
  35. [S5] L. C. SIEBENMANN, On detecting euclidean space homotopically among topological manifolds (Inventiones Math., vol. 6, 1968, p. 245-261). Zbl0169.55201MR38 #6601
  36. [S6] L. C. SIEBENMANN, On detecting open collars (Trans. Amer. Math. Soc., vol. 142, 1969, p. 201-227). Zbl0195.53802MR39 #7605
  37. [S7] L. C. SIEBENMANN, A total Whitehead torsion obstruction to fibering over the circle (Comment. Math. Helv., vol. 45, 1970, p. 1-48). Zbl0215.24603MR44 #4768
  38. [S8] L. C. SIEBENMANN, Infinite simple homotopy type (Indag. Math., 32, n° 5, 1970, p. 479-495). Zbl0203.56002MR44 #4746
  39. [S9] L. C. SIEBENMANN, Disruption of low-dimensional handlebody theory by Rohlin's theorem, p. 57-76 in Topology of Manifolds édité par J. C. CANTRELL et C. H. EDWARDS MARKHAM, Chicago, 1970. Zbl0281.57022MR42 #6836
  40. [S10] L. C. SIEBENMANN, Regular Open Neighborhoods, General Topology and its Application, vol. 3, 1973. Zbl0276.57003MR51 #6831
  41. [S11] L. C. SIEBENMANN, L'invariance topologique du type simple d'homotopie [d'après T. CHAPMAN et R. D. EDWARDS] (Séminaire Bourbaki, 1972-1973, exp. 428, Lecture Notes in Maths, 383, Springer Verlag, p. 195-210). Zbl0293.57007
  42. [SGH] L. C. SIEBENMANN, L. GUILLOU et H. HÄHL, Les voisinages ouverts réguliers (Ann. sci. Éc. Norm. Sup., 4e série, t. 6, 1973, p. 253-294). Zbl0294.57009MR48 #9732
  43. [St1] J. STALLINGS, The piecewise linear structure of euclidean space (Proc. Cambridge Phil. Soc., vol. 58, 1962, p. 481-488). Zbl0107.40203MR26 #6945
  44. [St2] J. STALLINGS, On topologically unknotted spheres (Ann. of Math.), vol. 77, 1963, p. 490-503). Zbl0121.18202MR26 #6946
  45. [Wa1] C. T. C. WALL, Finiteness conditions for CW-complexes (Ann. of Math., (2), vol. 81, 1965, p. 56-69). Zbl0152.21902MR30 #1515
  46. [Wa2] C. T. C. WALL, Finiteness conditions for CW-complexes II (Proc. Roy. Soc. (Great Britain), ser. A, vol. 295, 1966, p. 129-139). Zbl0152.21902MR35 #2283
  47. [Wb] C. WEBER, Quelques théorèmes bien connus sur les ANR et les CW-complexes (Enseignement Mathématique, (2), vol. 13, 1967, p. 211-222). Zbl0157.30002MR40 #6533
  48. [Ws] J. E. WEST, Mapping cylinders of Hilbert cube factors (Gen. Topology Appl., vol. 1, 1971, p. 111-125). Zbl0224.57004MR44 #5984
  49. [Z1] E. C. ZEEMAN, Seminar on combinatorial topology (mimeographed) Bures-sur-Yvette and U. of Warwick, 1963. 
  50. [Z2] E. C. ZEEMAN, The Poincaré conjecture for n ≧ 5, p. 198-204 in Topology of 3-manifolds, M. K. FORT Jr. Editor, Prentice-Hall, 1962. MR25 #3536
  51. [Z3] E. C. ZEEMAN, Unknotting combinatorial balls (Ann. of Math., vol. 78, 1963, p. 501-526). Zbl0122.17901MR28 #3432
  52. [Ω] T. CHAPMAN et L. SIEBENMANN, Finding a boundary for a Hilbert cube manifold, preprint, U. of Kentucky at Lexington, 1975. Zbl0361.57008

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.