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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Simplicial structure of the real analytic cut locus
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by Michael A. Buchner PDF
Proc. Amer. Math. Soc. 64 (1977), 118-121 Request permission

Abstract:

This note shows how to generalize to arbitrary dimensions the result of S.B. Myers that the cut locus in a real analytic Riemannian surface is triangulable. The basic tool is Hironaka’s theory of subanalytic sets.
References
  • Heisuke Hironaka, Subanalytic sets, Number theory, algebraic geometry and commutative algebra, in honor of Yasuo Akizuki, Kinokuniya, Tokyo, 1973, pp. 453–493. MR 0377101
  • Heisuke Hironaka, Triangulations of algebraic sets, Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29, Humboldt State Univ., Arcata, Calif., 1974) Amer. Math. Soc., Providence, R.I., 1975, pp. 165–185. MR 0374131
  • Sumner Byron Myers, Connections between differential geometry and topology. I. Simply connected surfaces, Duke Math. J. 1 (1935), no. 3, 376–391. MR 1545884, DOI 10.1215/S0012-7094-35-00126-0
  • Sumner Byron Myers, Connections between differential geometry and topology II. Closed surfaces, Duke Math. J. 2 (1936), no. 1, 95–102. MR 1545908, DOI 10.1215/S0012-7094-36-00208-9
  • J. Milnor, Morse theory, Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, N.J., 1963. Based on lecture notes by M. Spivak and R. Wells. MR 0163331
  • M. Buchner, Stability of the cut locus in dimensions $\leqslant 5$ (to appear).
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 64 (1977), 118-121
  • MSC: Primary 53C20; Secondary 32B20, 57D70
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0474133-5
  • MathSciNet review: 0474133