## 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