Decompositions of manifolds into codimension one submanifolds
Compositio Mathematica, Volume 55 (1985) no. 2, pp. 185-207.
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     author = {Daverman, R. J.},
     title = {Decompositions of manifolds into codimension one submanifolds},
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     pages = {185--207},
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     url = {http://archive.numdam.org/item/CM_1985__55_2_185_0/}
}
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Daverman, R. J. Decompositions of manifolds into codimension one submanifolds. Compositio Mathematica, Volume 55 (1985) no. 2, pp. 185-207. http://archive.numdam.org/item/CM_1985__55_2_185_0/

[1] F.D. Ancel and J.W. Cannon: The locally flat approximation of cell-like embedding relations. Ann. of Math. 109(2) (1979) 61-86. | MR | Zbl

[2] S. Armentrout: Cellular decompositions of 3-manifolds that yield 3-manifolds. Memoirs Amer. Math. Soc. 107 (1970). | MR | Zbl

[3] R.H. Bing: E3 does not contain uncountably many mutually exclusive surfaces. Bull. Amer. Math. Soc. 63 (1957) 404. Abstract # 60-801t.

[4] R.H. Bing: A surface is tame if its complement is 1-ULC. Trans. Amer. Math. Soc. 101 (1961) 294-305. | MR | Zbl

[5] M. Brown: Locally flat embeddings of topological manifolds. Ann. of Math. 75(2) (1962) 331-341. | MR | Zbl

[6] M. Brown: The monotone union of open n-cells is an open n-cell. Proc. Amer. Math. Soc. 12 (1961) 812-814. | MR | Zbl

[7] J.L. Bryant: Concerning uncountable families of n-cells in En. Michigan Math. J. 15 (1968) 477-479. | MR | Zbl

[8] A.V. Černavski: The equivalence of local flatness and local 1-connectedness for embeddings of (n-1)-dimensional manifolds in n-dimensional manifolds. Mat. Sb. 75(133) (1973) 279-286 [ = Math USSR Sb. 20 (1973) 297-304]. | MR | Zbl

[9] J. Cheeger and J.M. Kister: Counting topological manifolds. Topology 9 (1970) 149-151. | MR | Zbl

[10] E.H. Connell: A topological h-cobordism theorem for n > 5. Illinois J. Math. 11 (1967) 300-309. | MR | Zbl

[11] D.S. Coram: Approximate fibrations - a geometric perspective, in Shape Theory and Geometric Topology. S. Mardešić and J. Segal (ed.), Lecture Notes in Math., vol. 870, Berlin: Springer-Verlag (1981) 37-47. | MR | Zbl

[12] D.S. Coram and P.F. Duvalljr.: Approximate fibrations. Rocky Mountain J. Math. 7 (1977) 275-288. | MR | Zbl

[13] D.S. Coram and P.F. Duvalljr.: Mappings from S3 to S2 whose point inverses have the shape of a circle. Gen. Topology and its Appl. 9 (1979) 239-246. | Zbl

[14] R.J. Daverman: Locally nice codimension one manifolds are locally flat. Bull. Amer. Math. Soc. 79 (1973) 410-413. | MR | Zbl

[15] R.J. Daverman: Every crumpled n-cube is a closed n-cell-complement. Michigan Math. J. 24 (1977) 225-241. | MR | Zbl

[16] R.J. Daverman: Embedding phenomena based upon decomposition theory: wild Cantor sets satisfying strong homogeneity properties. Proc. Amer. Math. Soc. 75 (1979) 177-182. | MR | Zbl

[17] R.H. Fox and E. Artin: Some wild cells and spheres in three-dimensional space. Ann. of Math. 49 (2) (1948) 979-990. | MR | Zbl

[18] W. Haken: Some results on surfaces in 3-manifolds, in Studies in Modem Topology. P.J. Hilton (ed.), MAA Studies in Mathematics, Vol. 5, Prentice Hall, Englewood Cliffs, N.J. (1968) 39-98. | MR | Zbl

[19] N. Hosay: The sum of real cube and a crumpled cube is S3. Notices Amer. Math. Soc. 10 (1963) 666. Abstract # 607-17. See also errata 11 (1964) 152.

[20] L.S. Husch: Approximating approximate fibrations by fibrations. Can. J. Math. 29 (1977) 897-913. | MR | Zbl

[21] W. Jaco: Surfaces embedded in M2 X S1. Can. J. Math. 22 (1970) 553-568. | MR | Zbl

[22] V.-T. Liem: Manifolds accepting codimension one sphere-like decompositions, preprint. | Zbl

[23] L.L. Lininger: Some results on crumpled cubes. Trans. Amer. Math. Soc. 118 (1965) 534-549. | MR | Zbl

[24] D.R. Mcmillan Jr.: Neighborhoods of surfaces in 3-manifolds. Michigan Math. J. 14 (1967) 161-170. | MR | Zbl

[25] F. Quinn: Ends of Maps III: dimensions 4 and 5. Preprint Series 1982-83, No. 4, Aarhus Universitet Matematisk Institute. See also Addition to the same, preprint. | MR

[26] L.C. Siebenmann: Infinite simple homotopy types. Indag. Math. 32 (1970) 479-495. | MR | Zbl

[27] L.C. Siebenmann: Approximating cellular maps by homeomorphisms. Topology 11 (1973) 271-294. | MR | Zbl

[28] E.H. Spanier: Algebraic Topology. New York: McGraw-Hill Book Co (1966). | MR | Zbl