Les voisinages ouverts réguliers : critères homotopiques d'existence
Siebenmann, L. ; Guillou, L. ; Hähl, H.
Annales scientifiques de l'École Normale Supérieure, Tome 7 (1974), p. 431-461 / Harvested from Numdam
@article{ASENS_1974_4_7_3_431_0,
     author = {Siebenmann, Laurent and Guillou, Lucien and H\"ahl, H.},
     title = {Les voisinages ouverts r\'eguliers : crit\`eres homotopiques d'existence},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {7},
     year = {1974},
     pages = {431-461},
     doi = {10.24033/asens.1275},
     mrnumber = {50 \#14766},
     zbl = {0318.57011},
     mrnumber = {362324},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/ASENS_1974_4_7_3_431_0}
}
Siebenmann, L.; Guillou, L.; Hähl, H. Les voisinages ouverts réguliers : critères homotopiques d'existence. Annales scientifiques de l'École Normale Supérieure, Tome 7 (1974) pp. 431-461. doi : 10.24033/asens.1275. http://gdmltest.u-ga.fr/item/ASENS_1974_4_7_3_431_0/

[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). | MR 205212 | MR 34 #5045 | Zbl 0152.12601

[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). | MR 230284 | MR 37 #5847 | Zbl 0189.12402

[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). | MR 258064 | MR 41 #2711 | Zbl 0203.25805

[Bo1] K. Borsuk, Theory of Retracts, PWN, Warszawa, 1967. | MR 216473 | MR 35 #7306 | Zbl 0153.52905

[Bo2] K. Borsuk, Theory of shape, Aarhus Univ. (Lecture notes Séries, n° 28, 1971). | MR 293602 | MR 45 #2679 | Zbl 0232.55021

[Br] J. L. Bryant, Approximating embedding of polyhedra in codimension three (Trans. Amer. Math. Soc., vol. 170, 1972, p. 85-95). | MR 307245 | MR 46 #6365 | Zbl 0259.57007

[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). | MR 290376 | MR 44 #7560 | Zbl 0199.26703

[Ch1] T. Chapman, Compact Hilbert cube manifolds and the invariance of Whitehead torsion (Bull. Amer. Math. Soc., vol. 79, 1973, p. 52-56). | MR 346794 | MR 49 #11518 | Zbl 0251.57004

[Ch2] T. A. Chapman, Notices Amer. Math. Soc., vol. 19, 1972, p. A-810.

[Ch3] T. Chapman, Notes on Hilbert cube manifolds (miméo.) Univ. of Kentucky at Lexington, 1973.

[Co] M. M. Cohen, A general theory of relative regular neighborhoods (Trans. Amer. Math. Soc., vol. 136, 1969, p. 189-229). | MR 248802 | MR 40 #2052 | Zbl 0182.57602

[Do] A. Dold, Lectures on algebraic topology, Springer-Verlag, Berlin-Heidelberg-New-York, 1972. | MR 415602 | MR 54 #3685 | Zbl 0234.55001

[E] R. D. Edwards, Topological general position, preprint UCLA 1974.

[EW] S. Eilenberg et R. L. Wilder, Uniform local connectedness and contractibility (Amer. J. Math., vol. 64, 1942, p. 613-622). | MR 7100 | MR 4,87e | Zbl 0061.41103

[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]. | MR 423376 | Zbl 0231.57019

[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). | MR 27512 | MR 10,317g | Zbl 0033.13602

[F] R. H. Fox, On shape (Fund. Math., vol. 74, 1972, p. 47-71). | MR 296914 | MR 45 #5973 | Zbl 0232.55023

[GH] L. Guillou et H. Hähl, Les voisinages réguliers ouverts : critères homotopiques d'identification (à paraître). | Zbl 0344.57002

[He] D. W. Henderson, Infinite-dimentional manifolds are open subsets of Hilbert space (Topology, vol. 9, 1970, p. 25-33). | MR 250342 | MR 40 #3581 | Zbl 0167.51904

[Hd] J. F. P. Hudson, Piecewise-linear, Topology, W. A. Benjamin Inc., New-York et Amsterdam, 1969. | MR 248844 | MR 40 #2094 | Zbl 0189.54507

[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). | MR 286113 | Zbl 0169.55302

[J] F. E. A. Johnson, Lefschetz duality and topological neighbourhoods (Trans. Amer. Math. Soc., vol. 172, 1972, p. 95-110). | MR 310892 | MR 46 #9990 | Zbl 0264.57004

[KS1] R. C. Kirby et L. C. Siebenmann, Deformation of smooth and piecewise linear manifold structures II, Sliced families (preprint).

[KS2] R. C. Kirby et L. C. Siebenmann, Some basic theorems about topological manifolds (preprint).

[Mc1] D. R. Mc Millan Jr., UV-properties and related topics, Notes of B. J. SMITH (mimeographed) Florida State Univ., 1970.

[Mc2] D. R. Mc Millan Jr., A criterion for cellularity in a manifold II (Trans. Amer. Math. Soc., vol. 126, 1967, p. 217-224). | MR 208583 | MR 34 #8392 | Zbl 0155.31603

[Mil] R. T. Miller, Approximating codimension 3 embeddings (Ann. of Math., vol. 95, 1972, p. 406-416). | MR 46 #6366 | Zbl 0208.51801

[Mi1] J. W. Milnor, On spaces having the homotopy type of CW-complex (Trans. Amer. Math. Soc., vol. 90, 1959, p. 272-280). | MR 20 #6700 | Zbl 0084.39002

[Mi2] J. W. Milnor, Characteristic classes Notes, Appendix A, Princeton, Mars 1964.

[Sp] E. H. Spanier, Algebraic Topology, Mc Graw-Hill, 1966. | MR 35 #1007 | Zbl 0145.43303

[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).

[S2] L. C. Siebenmann, Version de [S1] (à paraître).

[S3] L. C. Siebenmann, Open regular neighborhoods of compacta (Notices Amer. Math. Soc., vol. 14, 1967, n° 67 T-26, p. 135).

[S4] L. C. Siebenmann, The structure of tame ends (Notices Amer. Math. Soc., vol. 13, 1966, n° 66 T-531, p. 862).

[S5] L. C. Siebenmann, On detecting euclidean space homotopically among topological manifolds (Inventiones Math., vol. 6, 1968, p. 245-261). | MR 38 #6601 | Zbl 0169.55201

[S6] L. C. Siebenmann, On detecting open collars (Trans. Amer. Math. Soc., vol. 142, 1969, p. 201-227). | MR 39 #7605 | Zbl 0195.53802

[S7] L. C. Siebenmann, A total Whitehead torsion obstruction to fibering over the circle (Comment. Math. Helv., vol. 45, 1970, p. 1-48). | MR 44 #4768 | Zbl 0215.24603

[S8] L. C. Siebenmann, Infinite simple homotopy type (Indag. Math., 32, n° 5, 1970, p. 479-495). | MR 44 #4746 | Zbl 0203.56002

[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. | MR 42 #6836 | Zbl 0281.57022

[S10] L. C. Siebenmann, Regular Open Neighborhoods, General Topology and its Application, vol. 3, 1973. | MR 51 #6831 | Zbl 0276.57003

[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). | Numdam | Zbl 0293.57007

[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). | Numdam | MR 48 #9732 | Zbl 0294.57009

[St1] J. Stallings, The piecewise linear structure of euclidean space (Proc. Cambridge Phil. Soc., vol. 58, 1962, p. 481-488). | MR 26 #6945 | Zbl 0107.40203

[St2] J. Stallings, On topologically unknotted spheres (Ann. of Math.), vol. 77, 1963, p. 490-503). | MR 26 #6946 | Zbl 0121.18202

[Wa1] C. T. C. Wall, Finiteness conditions for CW-complexes (Ann. of Math., (2), vol. 81, 1965, p. 56-69). | MR 30 #1515 | Zbl 0152.21902

[Wa2] C. T. C. Wall, Finiteness conditions for CW-complexes II (Proc. Roy. Soc. (Great Britain), ser. A, vol. 295, 1966, p. 129-139). | MR 35 #2283 | Zbl 0152.21902

[Wb] C. Weber, Quelques théorèmes bien connus sur les ANR et les CW-complexes (Enseignement Mathématique, (2), vol. 13, 1967, p. 211-222). | MR 40 #6533 | Zbl 0157.30002

[Ws] J. E. West, Mapping cylinders of Hilbert cube factors (Gen. Topology Appl., vol. 1, 1971, p. 111-125). | MR 44 #5984 | Zbl 0224.57004

[Z1] E. C. Zeeman, Seminar on combinatorial topology (mimeographed) Bures-sur-Yvette and U. of Warwick, 1963. | Zbl 0179.52402

[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. | MR 25 #3536 | Zbl 1246.57032

[Z3] E. C. Zeeman, Unknotting combinatorial balls (Ann. of Math., vol. 78, 1963, p. 501-526). | MR 28 #3432 | Zbl 0122.17901

[Ω] T. Chapman et L. Siebenmann, Finding a boundary for a Hilbert cube manifold, preprint, U. of Kentucky at Lexington, 1975. | Zbl 0361.57008