Geodesic
Coincidence of local flatness and local simple-connectedness for embeddings of $(n-1)$-dimensional manifolds in $n$-dimensional manifolds when $n>4$
Sbornik. Mathematics, Tome 20 (1973) no. 2, pp. 297-304 
A. V. Chernavskii. Coincidence of local flatness and local simple-connectedness for embeddings of $(n-1)$-dimensional manifolds in $n$-dimensional manifolds when $n>4$. Sbornik. Mathematics, Tome 20 (1973) no. 2, pp. 297-304. http://geodesic.mathdoc.fr/item/SM_1973_20_2_a6/
@article{SM_1973_20_2_a6,
     author = {A. V. Chernavskii},
     title = {Coincidence of local flatness and local simple-connectedness for embeddings of $(n-1)$-dimensional manifolds in $n$-dimensional manifolds when~$n>4$},
     journal = {Sbornik. Mathematics},
     pages = {297--304},
     year = {1973},
     volume = {20},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_20_2_a6/}
}
TY  - JOUR
AU  - A. V. Chernavskii
TI  - Coincidence of local flatness and local simple-connectedness for embeddings of $(n-1)$-dimensional manifolds in $n$-dimensional manifolds when $n>4$
JO  - Sbornik. Mathematics
PY  - 1973
SP  - 297
EP  - 304
VL  - 20
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1973_20_2_a6/
LA  - en
ID  - SM_1973_20_2_a6
ER  - 
%0 Journal Article
%A A. V. Chernavskii
%T Coincidence of local flatness and local simple-connectedness for embeddings of $(n-1)$-dimensional manifolds in $n$-dimensional manifolds when $n>4$
%J Sbornik. Mathematics
%D 1973
%P 297-304
%V 20
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1973_20_2_a6/
%G en
%F SM_1973_20_2_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

The result formulated in the title is proved. Bibliography: 26 titles.

[1] M. Brown, “Locally flat imbeddings of topological manifolds”, Ann. Math., 75:2 (1962), 331–342 | DOI | MR

[2] S. Eilenberg, R. L. Wilder, “Uniform local connectedness and contractibility”, Amer. J. Math., 64:4 (1942), 613–622 | DOI | MR | Zbl

[3] O. G. Harrold, “Euclidean domains with uniformly abelian locally fundamental groups”, Trans. Amer. Math. Soc., 67:1 (1949), 120–129 | DOI | MR | Zbl

[4] R. H. Bing, “A surface is tame if its complement is I-ULC”, Trans. Amer. Math. Soc., 101:2 (1961), 294–305 | DOI | MR | Zbl

[5] R. H. Bing, “Tame Cantor sets in $E^3$”, Pacific J. Math., 11:2 (1961), 435–446 | MR | Zbl

[6] T. Homma, “On tame imbedding of 0-dimensional compact sets in $E^3$”, Yokahama Math. J., 7:2 (1959), 191–195 | MR | Zbl

[7] J. R. Stallings, “The piecewise linear structure of euclidean space”, Proc. Cambr. Phil. Soc., 58:3 (1962), 481–488 | DOI | MR | Zbl

[8] J. P. Hempel, D. R. McMillan, “Locally nice embeddings of manifolds”, Amer. J. Math., 88:1 (1966), 1–19 | DOI | MR | Zbl

[9] D. R. McMillan, “Taming Cantor sets in $E^n$”, Bull. Amer. Math. Soc., 70:5 (1964), 706–708 | DOI | MR | Zbl

[10] J. L. Bryant, C. L. Seebeck, “Locally nice embeddings of polyhedra”, Quart. J. Math., 19:75 (1968), 257–284 | DOI | MR

[11] A. V. Chernavskii, “Topologicheskie vlozheniya mnogoobrazii”, DAN SSSR, 187:6 (1969), 1247–1250

[12] M. A. Shtanko, “Vlozhenie kompaktov v evklidovo prostranstvo”, DAN SSSR, 198:4 (1971), 783–786

[13] M. A. Shtanko, “Approksimatsiya vlozhenii kompaktov v korazmernosti bolshe dvukh”, DAN SSSR, 198:4 (1971), 783–786

[14] L. Siebenmann, “Approximating cellular mappings by homeomorphisms”, Topology, 11:3 (1972), 271–294 | DOI | MR | Zbl

[15] M. Brown, “A proof of the generalized Schoenflies theorem”, Bull. Amer. Math. Soc., 66:2 (1960), 74–76 | DOI | MR | Zbl

[16] D. R. McMillan, “A criterion for cellularity in a manifold”, Ann. Math., 79:2 (1964), 327–337 | DOI | MR | Zbl

[17] V. P. Kompaniets, “Gomotopicheskii kriterii tochechnogo otobrazheniya”, Ukr. matem. zh., 18:4 (1966), 3–10 | MR | Zbl

[18] Van Ny Kyong, “Psevdoizotopiya trekhmernoi sfery $S^3$”, DAN SSSR, 199:5 (1971), 1002–1003 | Zbl

[19] St. Armentrout, “Cellular decomposition of 3-manifolds that yield 3-manifolds”, Mem. Amer. Math. Soc., 107 (1971), 1–72 | MR

[20] R. Kirby, “Stable homeomorphisms and the annulus conjecture”, Ann. Math., 80 (1969), 575–582 | DOI | MR

[21] C. L. Seebeck, “Collaring an $(n-1)$-manifold in an $n$-manifolds”, Trans. Amer. Math. Soc., 148:1 (1970), 63–68 | DOI | MR | Zbl

[22] R. T. Miller, “Approximating codimension 3 embeddings”, Ann. Math., 95:3 (1972), 406–416 | DOI | MR | Zbl

[23] R. H. Bing, “Radial engulfing”, Conf. on the topol. of manif., ed. P. Hocking, 1968, 1–19 | MR

[24] R. J. Daverman, “Locally nice codimension one manifolds are locally flat, ab. 72-T-G 172”, Notices Amer. Math. Soc., 19:6 (1972), A–724 | MR

[25] A. Černavskii, “Espace de plongements”, Actes du Congrès Int. des Math. 1970, t. 2, 1971, 65–67 | MR

[26] L. C. Siebenmann, “Topological manifolds”, Actes du Congrès Int. des Math. 1970, t. 2, 1971, 133–163 | MR | Zbl