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).
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