Les voisinages ouverts réguliers : critères homotopiques d'existence

 Access to full text

 Full (PDF)

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 > 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

1. L. S. Husch, I. Ivanšić, Shape domination and embedding up to shape
2. Laurent Siebenmann, Amorces de la chirurgie en dimension quatre : un $S^3\times R$ exotique
3. L. Guillou, H. Hähl, Les voisinages réguliers ouverts : critères homotopiques d'identification