Arcs in the Hilbert cube (S n ) whose complements have different fundamental groups
Daverman, R. J. ; Singh, S.
Compositio Mathematica, Tome 50 (1983), p. 209-222 / Harvested from Numdam
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Publié le : 1983-01-01
@article{CM_1983__48_2_209_0,
     author = {Daverman, R. J. and Singh, S.},
     title = {Arcs in the Hilbert cube $(S^n)$ whose complements have different fundamental groups},
     journal = {Compositio Mathematica},
     volume = {50},
     year = {1983},
     pages = {209-222},
     mrnumber = {700004},
     zbl = {0522.57012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1983__48_2_209_0}
}

Daverman, R. J.; Singh, S. Arcs in the Hilbert cube $(S^n)$ whose complements have different fundamental groups. Compositio Mathematica, Tome 50 (1983) pp. 209-222. http://gdmltest.u-ga.fr/item/CM_1983__48_2_209_0/

[AC] J.J. Andrews and M.L. Curtis: n-Space Modulo an Arc, Ann. of Math. 75 (1962), 1-7. | MR 139153 | Zbl 0105.17403

[AR] A.V. Arhangel'Skii: Structure and classification of topological spaces and cardinal invariants, Russian Math. Surveys 33 (1978), 33-96. | MR 526012 | Zbl 0428.54002

[AP] S. Armentrout and T.M. Price: Homotopy Properties of Decomposition Spaces, Trans. Amer. Math. Soc. 143 (1969), 499-507. | MR 273574 | Zbl 0195.25504

[AF] E. Artin and R.H. Fox: Some Wild Cells and Spheres in Three-Dimensional Space, Ann. of Math. 49 (1948), 979-990. | MR 27512 | Zbl 0033.13602

[B] K. Borsuk: Theory of Retracts, PWN, Warsaw, 1967. | MR 216473 | Zbl 0153.52905

[BA] C.D. Bass: Some products of topological spaces which are manifolds, Proc. Amer. Math. Soc. 81 (1981), 641-646. | MR 601746 | Zbl 0466.57006

[BR] M. Brown: Wild Cells and Spheres in Higher Dimensions, Mich. Math. J. 14 (1967), 219-224. | MR 221481 | Zbl 0147.23902

[C1] J.W. Cannon: Shrinking Cell-like Decompositions of Manifolds. Codimension Three, Ann. of Math. 110 (1979), 83-112. | MR 541330 | Zbl 0424.57007

[C2] J.W. Cannon: The Recognition Problem: What is a Topological n-Manifold?, Bull. Amer. Math. Soc. 84 (1978), 832-866. | MR 494113 | Zbl 0418.57005

[CH] T.A. Chapman: Lectures on Hilbert Cube Manifolds, CBMS Regional Conf. Series in Math., no. 28, Amer. Math. Soc., Providence, R.I., 1976. | MR 423357 | Zbl 0347.57005

[D1] R.J. Daverman: Infinite Inflations of Crumpled Cubes, Topology and Its Appl. 12 (1981), 35-43. | MR 600461 | Zbl 0447.57009

[D2] R.J. Daverman: Sewings of Closed n-cell Complements, Trans. Amer. Math. Soc., to appear.

[D3] R.J. Daverman: Embeddings of (n - 1)-spheres in Euclidean n-Space, Bull. Amer. Math. Soc. 84 (1978), 377-405. | MR 645404 | Zbl 0391.57014

[DE] R.J. Daverman and W.T. Eaton: Each Disk in En Can be Squeezed to An Arc, preprint.

[E] R.D. Edwards: The topology of manifolds and cell-like maps, in Proceedings of the International Congress of Mathematicians, Helsinki, 1978 (O. Lehto, editor), Adacemia Scientarium Fennica, Helsinki, 1980, 111-127. | MR 562601 | Zbl 0428.57004

[DW] R.D. Edwards and J.J. Walsh: Čech Homology Characterizations of Infinite Dimensional Manifolds, Amer. J. Math. 103 (1981), 411-435. | MR 618319 | Zbl 0538.57006

[G1] L.C. Glaser: Euclidean (q + r)-Space Modulo an r-Plane of Collapsible p-Complexes, Trans. Amer. Math. Soc. 157 (1971), 261-278. | MR 276943 | Zbl 0217.49102

[G2] L.C. Glaser: Geometric Combinatorial Topology, Vol. II, Van Nostrand and Reinhold Co., London-New York, 1972. | Zbl 0229.57010

[K] A.G. Kurosh: The Theory of Groups, Vol. II, Chelsea Publishing Co., New York, 1956. | MR 80089 | Zbl 0064.25104

[L] R.C. Lacher: Cell-Like Mappings and Their Generalizations, Bull. Amer. Math. Soc. 83 (1977), 495-552. | MR 645403 | Zbl 0364.54009

[M] W.S. Massey: Algebraic Topology: An Introduction, Harcourt, Brace and World, New York, 1967. | MR 211390 | Zbl 0153.24901

[ME] D.V. Meyer: More decompositions of En which are factors of En+1, Fund. Math. 67 (1970), 49-65. | MR 263052 | Zbl 0194.55801

[R] H. Roslaniec: On Decompositions Spaces of En with Small Homeomorphism Group, Bull. Acad. Polon. Sciences 24 (1976), 901-904. | MR 474307 | Zbl 0342.54007

[S1] S. Singh: Generalized Manifolds (ANR's and AR's) and Null Decompositions of Manifolds, Fund. Math., to appear. | MR 690670 | Zbl 0537.57009

[S2] S. Singh: Decompositions of the Hilbert Cube Manifolds and ANR's, in preparation.

[T] H. Torúnczyk: On CE Images of the Hilbert Cube and Characterizations of Q-Manifolds, Fund. Math. 106 (1980), 31-40. | MR 585543 | Zbl 0346.57004

[VM] J. Van Mill: A rigid space X for which X x X is homogeneous: an application of infinite dimensional topology, Proc. Amer. Math. Soc. 83 (1981), 597-600. | MR 627701 | Zbl 0484.54032

[W] R.L. Wilder: Monotone mappings of manifolds, Pacific J. Math. 7 (1957), 1519-1528. | MR 92966 | Zbl 0086.37302

[WO] R.Y.T. Wong: A wild cantor set in the Hilbert Cube, Pacific J. Math. 24 (1968), 189-193. | MR 221487 | Zbl 0163.45003