Largest normal neighborhoods
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- Proc. Amer. Math. Soc. 61 (1976), 99-101 Request permission
Abstract:
It is well known that the largest normal neighborhood of a point in a compact Riemannian manifold is a Euclidean cell, that is, homeomorphic to the open unit ball. In this paper it is proved that this normal neighborhood is in fact ${C^\infty }$ diffeomorphic to the open unit ball. The method is to paste together a sequence of ${C^\infty }$ radial dilations which combine to engulf an open ball or all of ${{\mathbf {R}}^n}$.References
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S. Kobayashi and K. Nomizu, Foundations of differential geometry, Vol. 2, Interscience, New York, 1969. MR 38 #6501.
- Edwin E. Moise, Affine structures in $3$-manifolds. V. The triangulation theorem and Hauptvermutung, Ann. of Math. (2) 56 (1952), 96–114. MR 48805, DOI 10.2307/1969769
- James Munkres, Obstructions to the smoothing of piecewise-differentiable homeomorphisms, Ann. of Math. (2) 72 (1960), 521–554. MR 121804, DOI 10.2307/1970228
- John Stallings, The piecewise-linear structure of Euclidean space, Proc. Cambridge Philos. Soc. 58 (1962), 481–488. MR 149457
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 61 (1976), 99-101
- MSC: Primary 57D70; Secondary 53C20
- DOI: https://doi.org/10.1090/S0002-9939-1976-0431220-4
- MathSciNet review: 0431220