Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Sticky arcs in $ E\sp{n}$ $ (n\geq 4)$


Author: David G. Wright
Journal: Proc. Amer. Math. Soc. 66 (1977), 181-182
MSC: Primary 57A15; Secondary 55A35
DOI: https://doi.org/10.1090/S0002-9939-1977-0515648-0
MathSciNet review: 0515648
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let A and B be arcs in $ {E^3}$, Euclidean 3-space. Then A can be ``slipped'' off B; i.e., there exists a homeomorphism of $ {E^3}$ onto itself, arbitrarily close to the identity, such that $ h(A) \cap B = \emptyset $. The purpose of this note is to show that arcs in $ {E^n}(n \geqslant 4)$ do not always enjoy this property. The examples depend heavily on a recent result of McMillan.


References [Enhancements On Off] (What's this?)

  • [1] S. Armentrout, Decompositions of $ {E^3}$ with a compact 0-dimensional set of nondegenerate elements, Trans. Amer. Math. Soc. 123 (1966), 165-177. MR 0195074 (33:3279)
  • [2] M. Brown, A proof of the generalized Schoenflies theorem, Bull. Amer. Math. Soc. 66 (1960), 74-76. MR 0117695 (22:8470b)
  • [3] R. D. Edwards and R. C. Kirby, Deformations of spaces of imbeddings, Ann. of Math. (2) 93 (1971), 63-88. MR 0283802 (44:1032)
  • [4] D. R. McMillan, Jr., An arc in a PL n-manifold with no neighborhood that embeds in $ {S^n}, n \geqslant 4$ Michigan Math. J. (to appear). MR 0482772 (58:2825)
  • [5] -, A criterion for cellularity in a manifold. II Trans. Amer. Math. Soc. 126 (1967), 217-224. MR 0208583 (34:8392)
  • [6] C. L. Seebeck, III, Collaring an $ (n - 1)$-manifold in an n-manifold, Trans. Amer. Math. Soc. 148 (1970), 63-68. MR 0258045 (41:2692)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57A15, 55A35

Retrieve articles in all journals with MSC: 57A15, 55A35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0515648-0
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society