Decompositions of manifolds into codimension one submanifolds
Compositio Mathematica, Volume 55 (1985) no. 2, p. 185-207
@article{CM_1985__55_2_185_0,
     author = {Daverman, R. J.},
     title = {Decompositions of manifolds into codimension one submanifolds},
     journal = {Compositio Mathematica},
     publisher = {Martinus Nijhoff Publishers},
     volume = {55},
     number = {2},
     year = {1985},
     pages = {185-207},
     zbl = {0593.57005},
     mrnumber = {795714},
     language = {en},
     url = {http://www.numdam.org/item/CM_1985__55_2_185_0}
}
Daverman, R. J. Decompositions of manifolds into codimension one submanifolds. Compositio Mathematica, Volume 55 (1985) no. 2, pp. 185-207. http://www.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 519353 | Zbl 0405.57007

[2] S. Armentrout: Cellular decompositions of 3-manifolds that yield 3-manifolds. Memoirs Amer. Math. Soc. 107 (1970). | MR 413104 | Zbl 0221.57003

[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 131265 | Zbl 0109.15406

[5] M. Brown: Locally flat embeddings of topological manifolds. Ann. of Math. 75(2) (1962) 331-341. | MR 133812 | Zbl 0201.56202

[6] M. Brown: The monotone union of open n-cells is an open n-cell. Proc. Amer. Math. Soc. 12 (1961) 812-814. | MR 126835 | Zbl 0103.39305

[7] J.L. Bryant: Concerning uncountable families of n-cells in En. Michigan Math. J. 15 (1968) 477-479. | MR 238285 | Zbl 0175.20603

[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 334222 | Zbl 0286.57005

[9] J. Cheeger and J.M. Kister: Counting topological manifolds. Topology 9 (1970) 149-151. | MR 256399 | Zbl 0199.58403

[10] E.H. Connell: A topological h-cobordism theorem for n > 5. Illinois J. Math. 11 (1967) 300-309. | MR 212808 | Zbl 0146.45201

[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 643521 | Zbl 0493.57006

[12] D.S. Coram and P.F. Duvalljr.: Approximate fibrations. Rocky Mountain J. Math. 7 (1977) 275-288. | MR 442921 | Zbl 0367.55019

[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 0417.54014

[14] R.J. Daverman: Locally nice codimension one manifolds are locally flat. Bull. Amer. Math. Soc. 79 (1973) 410-413. | MR 321095 | Zbl 0256.57005

[15] R.J. Daverman: Every crumpled n-cube is a closed n-cell-complement. Michigan Math. J. 24 (1977) 225-241. | MR 488066 | Zbl 0376.57007

[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 529237 | Zbl 0407.57011

[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 27512 | Zbl 0033.13602

[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 224071 | Zbl 0194.24902

[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 500990 | Zbl 0366.55006

[21] W. Jaco: Surfaces embedded in M2 X S1. Can. J. Math. 22 (1970) 553-568. | MR 267596 | Zbl 0205.53501

[22] V.-T. Liem: Manifolds accepting codimension one sphere-like decompositions, preprint. | Zbl 0582.57009

[23] L.L. Lininger: Some results on crumpled cubes. Trans. Amer. Math. Soc. 118 (1965) 534-549. | MR 178460 | Zbl 0134.43002

[24] D.R. Mcmillan Jr.: Neighborhoods of surfaces in 3-manifolds. Michigan Math. J. 14 (1967) 161-170. | MR 212778 | Zbl 0148.17702

[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 679069

[26] L.C. Siebenmann: Infinite simple homotopy types. Indag. Math. 32 (1970) 479-495. | MR 287542 | Zbl 0203.56002

[27] L.C. Siebenmann: Approximating cellular maps by homeomorphisms. Topology 11 (1973) 271-294. | MR 295365 | Zbl 0216.20101

[28] E.H. Spanier: Algebraic Topology. New York: McGraw-Hill Book Co (1966). | MR 210112 | Zbl 0145.43303