Simplicial structure of the real analytic cut locus

Author:
Michael A. Buchner

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

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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.

**[1]**H. Hironaka,*Subanalytic sets in number theory, algebraic geometry and commutative algebra*, Papers in honor of Y. Akizuki, Kinokuniya, Tokyo, 1973, pp. 453-493. MR**0377101 (51:13275)****[2]**-,*Triangulations of algebraic sets*, Proc. Sympos. Pure Math., vol. 29, Amer. Math. Soc., Providence, R.I., 1975, pp. 165-185. MR**51**#10331. MR**0374131 (51:10331)****[3]**Sumner B. Myers,*Connections between differential geometry and topology*. I:*Simply connected surfaces*, Duke Math. J.**1**(1935), 376-391. MR**1545884****[4]**-,*Connections between differential geometry and topology*. II:*Closed surfaces*, Duke Math. J.**2**(1936), 95-102. MR**1545908****[5]**J. Milnor,*Morse theory*, Ann. of Math. Studies, no. 51, Princeton Univ. Press, Princeton, N.J., 1963. MR**29**#634. MR**0163331 (29:634)****[6]**M. Buchner,*Stability of the cut locus in dimensions*(to appear).

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DOI:
https://doi.org/10.1090/S0002-9939-1977-0474133-5

Article copyright:
© Copyright 1977
American Mathematical Society