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Les voisinages réguliers ouverts: critères homotopiques d’identification. (French) Zbl 0344.57002

MSC:
57N40 Neighborhoods of submanifolds
55P10 Homotopy equivalences in algebraic topology
55Q05 Homotopy groups, general; sets of homotopy classes
57N15 Topology of the Euclidean \(n\)-space, \(n\)-manifolds (\(4 \leq n \leq \infty\)) (MSC2010)
57N30 Engulfing in topological manifolds
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References:
[1] K. Borsuk : Theory of retracts. Monografie Matematyczne tom 44 , Polish Scientific publishers, Warszawa (1967). · Zbl 0153.52905
[2] K. Borsuk : Concerning homotopy properties of compacta . Fund. Math. 62 (1968) 223-254. · Zbl 0159.24603 · eudml:214016
[3] E. Brown : Unknotting in M2\times I. Trans . Amer. Math. Soc. 123 (1966) 480-505. · Zbl 0151.32903 · doi:10.2307/1994670
[4] E. Connel : A topological h-cobordism for n \? 5 . Illinois J. of Math. Il (1967) 300-309. · Zbl 0146.45201
[5] R. Fox : On shape . Fund. Math. 74 (1972) 47-71 et idem 75 (1972) 85. · Zbl 0232.55023 · eudml:214415
[6] M. Goldman : An algebraic classification of non compact 2-manifolds . Trans. Amer. Math. Soc. 156 (1971) 241-258. · Zbl 0232.57007 · doi:10.2307/1995610
[7] S. Hu : Theory of retracts . Wayne State Univ. Press, Detroit (1965). · Zbl 0145.43003
[8] L. Hush and T. Price : Finding a boundary for a 3-manifold . Ann. of Math. (2) 91 (1970) 223-235 et idem (2) 93 (1971) 486-488. · Zbl 0169.55302 · doi:10.2307/1970605
[9] S. Ichiraku and M. Kato : On higher-dimensional strings of codimension two . Quart. J. of Math. 23 (1972) 239-248. · Zbl 0242.57008 · doi:10.1093/qmath/23.3.239
[10] M. Mardesic and J. Segal : Shape of compacta and ANR-systems . Fund. Math. 72 (1971) 41-59 et 61-68. · Zbl 0222.55018 · eudml:214362
[11] J. Milnor : On space having the homotopy type of a CW complex . Trans. Amer. Math. Soc. 90 (1959) 272-280. · Zbl 0084.39002 · doi:10.2307/1993204
[12] M. Newman : The engulfing theorem for topological manifolds . Ann. of Math. (2) 84 (1966) 555-571. · Zbl 0166.19801 · doi:10.2307/1970460
[13] L. Siebenmann : The obstruction to finding a boundary for an open manifold of dimension \? 5 . Thesis, Princeton (1965).
[14] L. Siebenmann : Nouvelle version de [13] (à paraître).
[15] L. Siebenmann : On detecting open collars . Trans. Amer. Math. Soc. 142 (1969) 201-227. · Zbl 0195.53802 · doi:10.2307/1995353
[16] L. Siebenmann : On detecting euclidean space homotopically among topological manifolds . Inventiones Math. 6 (1968) 245-261. · Zbl 0169.55201 · doi:10.1007/BF01404826 · eudml:141943
[17] L. Siebenmann : Deformation of homeomorphisms on stratified sets . Comment. Math. Helv. 47 (1972) 123-163. · Zbl 0252.57012 · doi:10.1007/BF02566793 · eudml:139504
[18] L. Siebenmann : Regular open neighbourhoods . General Topology and its applications 3 (1973) 51-61. · Zbl 0276.57003 · doi:10.1016/0016-660X(73)90030-5
[19] L. Siebenmann , L. Guillou , H. Hähl : Les voisinages ouverts réguliers . Ann. Ecole Normale Sup. (4) 6 (1973) 253-293. · Zbl 0294.57009 · doi:10.24033/asens.1248 · numdam:ASENS_1973_4_6_2_253_0 · eudml:81917
[20] L. Siebenmann , L. Guillou , H. Hähl : Les voisinages ouverts réguliers: Critères homotopiques d’existence . Ann. Ecole Normale Sup. (4) 7 (1974) 431-462. · Zbl 0318.57011 · doi:10.24033/asens.1275 · numdam:ASENS_1974_4_7_3_431_0 · eudml:81944
[21] E. Spanier : Algebraic Topology . McGraw-Hill Inc. (1966). · Zbl 0145.43303
[22] J. Stallings : The piecewise linear structure of euclidean space , Proc. Camb. Phil. Soc. 58 (1962) 481-488. · Zbl 0107.40203
[23] J. Stallings : On topologically unknotted spheres . Ann. of Math. (2) 77 (1963) 490-503. · Zbl 0121.18202 · doi:10.2307/1970127
[24] J. Stallings : On infinite processes leading to differentiability in the complement of a point , pp. 245-254 in Differential and Combinatorial Topology : a symposium in honor of Marston Morse. Princeton Univ. Press, N.J. (1965). · Zbl 0136.44302
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