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A class of embeddings of $ S\sp{n-1}$ and $ B\sp{n}$ in $ R\sp{n}$


Authors: J. C. Cantrell, T. M. Price and T. B. Rushing
Journal: Proc. Amer. Math. Soc. 29 (1971), 208-210
MSC: Primary 57.05
DOI: https://doi.org/10.1090/S0002-9939-1971-0275445-5
MathSciNet review: 0275445
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Abstract: We show that if D is an n or $ (n - 1)$-cell in $ {R^n},n > 4$, and E is an $ (n - 2)$-cell in Bd D, with $ D - E$ locally flat in $ {R^n}$ and E locally flat in each of Bd D and $ {R^n}$, then D is locally flat in $ {R^n}$.


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

  • [1] J. C. Cantrell and R. C. Lacher, Local flattening of a submanifold, Quart. J. Math. Oxford Ser. (2) 20 (1969), 1-10, MR 39 #955. MR 0239598 (39:955)
  • [2] -, Some local flatness criteria for low codimensional submanifolds, Quart. J. Math. Oxford Ser. 82 (1970), 129-136. MR 0261608 (41:6221)
  • [3] T. B. Rushing, Everywhere wild cells and spheres, Rocky Mt. J. Math. (to appear). MR 0301741 (46:896)
  • [4] 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)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0275445-5
Keywords: Local flatness, collared submanifolds, 1-SS, 1-LC
Article copyright: © Copyright 1971 American Mathematical Society

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