Proceedings of the American Mathematical Society

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

 

 

Crumpled cubes that are not highly complex


Author: Robert J. Daverman
Journal: Proc. Amer. Math. Soc. 71 (1978), 325-328
MSC: Primary 57N50
MathSciNet review: 500515
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Abstract: It is proved that any crumpled n-cube $ C,n \geqslant 5$, whose wildness is contained in an $ (n - 2)$-manifold S in Bd C must be of Type 2, which is to say that its wildness, though possibly complicated, is not incredibly complicated.


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

  • [1] F. D. Ancel and J. W. Cannon, The locally flat approximation of cell-like embedding relations (to appear). MR 519353 (81f:57009)
  • [2] R. H. Bing, Retractions onto spheres, Amer. Math. Monthly 71 (1964), 481-484. MR 0162236 (28:5435)
  • [3] R. J. Daverman, Pushing an $ (n - 1)$-sphere in $ {S^n}$ almost into its complement, Duke Math. J. 39 (1972), 719-723. MR 0314055 (47:2607)
  • [4] -, Sewings of closed n-cell-complements, Trans. Amer. Math. Soc. (to appear).
  • [5] -, Every crumpled n-cube is a closed n-cell-complement, Michigan Math. J. 24 (1977), 225-241. MR 0488066 (58:7637)
  • [6] C. L. Seebeck III, Tame arcs on wild cells, Proc. Amer. Math. Soc. 29 (1971), 197-201. MR 0281177 (43:6896)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0500515-X
Keywords: Wild embedding, locally flat embedding, crumpled cube, closed n-cell-complement, 1-ULC
Article copyright: © Copyright 1978 American Mathematical Society