A collaring theorem for codimension one manifolds
HTML articles powered by AMS MathViewer
- by Robert J. Daverman and Fred C. Tinsley
- Proc. Amer. Math. Soc. 120 (1994), 969-972
- DOI: https://doi.org/10.1090/S0002-9939-1994-1205486-8
- PDF | Request permission
Abstract:
The chief result implies that an $n$-manifold $S$ embedded in the interior of an $(n + 1)$-manifold $M$ as a closed, separating subset is locally flatly embedded if the embedding is well behaved in a locally peripheral sense and if $S$ has arbitrarily close neighborhoods $Q$ such that the fundamental groups of appropriate components of $Q\backslash S$ admit a uniform finite upper bound on the number of generators.References
- C. E. Burgess, Criteria for a $2$-sphere in $S^{3}$ to be tame modulo two points, Michigan Math. J. 14 (1967), 321โ330. MR 216481
- J. C. Cantrell, Almost locally flat embeddings of $S^{n-1}$ in $S^{n}$, Bull. Amer. Math. Soc. 69 (1963), 716โ718. MR 154288, DOI 10.1090/S0002-9904-1963-10998-2
- A. V. ฤernavskiฤญ, The identity of local flatness and local simple connectedness for imbeddings of $(n-1)$-dimensional into $n$-dimensional manifolds when $n>4$, Mat. Sb. (N.S.) 91(133) (1973), 279โ286, 288 (Russian). MR 0334222
- R. J. Daverman, Non-homeomorphic approximations of manifolds with surfaces of bounded genus, Duke Math. J. 37 (1970), 619โ625. MR 267546
- Robert J. Daverman, Locally nice codimension one manifolds are locally flat, Bull. Amer. Math. Soc. 79 (1973), 410โ413. MR 321095, DOI 10.1090/S0002-9904-1973-13190-8
- Robert J. Daverman, Every crumpled $n$-cube is a closed $n$-cell-complement, Michigan Math. J. 24 (1977), no.ย 2, 225โ241. MR 488066
- R. J. Daverman, Decompositions of manifolds into codimension one submanifolds, Compositio Math. 55 (1985), no.ย 2, 185โ207. MR 795714
- Robert J. Daverman, Each crumpled $4$-cube is a closed $4$-cell-complement, Topology Appl. 26 (1987), no.ย 2, 107โ113. MR 896866, DOI 10.1016/0166-8641(87)90061-7
- R. J. Daverman and F. C. Tinsley, Laminations, finitely generated perfect groups, and acyclic maps, Michigan Math. J. 33 (1986), no.ย 3, 343โ351. MR 856526, DOI 10.1307/mmj/1029003414
- R. J. Daverman and F. C. Tinsley, A controlled plus construction for crumpled laminations, Trans. Amer. Math. Soc. 342 (1994), no.ย 2, 807โ826. MR 1182981, DOI 10.1090/S0002-9947-1994-1182981-6
- Ralph H. Fox and Emil Artin, Some wild cells and spheres in three-dimensional space, Ann. of Math. (2) 49 (1948), 979โ990. MR 27512, DOI 10.2307/1969408
- Robion C. Kirby, On the set of non-locally flat points of a submanifold of codimension one, Ann. of Math. (2) 88 (1968), 281โ290. MR 236900, DOI 10.2307/1970575
- William S. Massey, Algebraic topology: an introduction, Graduate Texts in Mathematics, Vol. 56, Springer-Verlag, New York-Heidelberg, 1977. Reprint of the 1967 edition. MR 0448331
- Frank Quinn, Ends of maps. III. Dimensions $4$ and $5$, J. Differential Geometry 17 (1982), no.ย 3, 503โ521. MR 679069
Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 969-972
- MSC: Primary 57N45; Secondary 57N35, 57N40, 57N70
- DOI: https://doi.org/10.1090/S0002-9939-1994-1205486-8
- MathSciNet review: 1205486