Simplicial structure of the real analytic cut locus
Author:
Michael A. Buchner
Journal:
Proc. Amer. Math. Soc. 64 (1977), 118121
MSC:
Primary 53C20; Secondary 32B20, 57D70
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]
Heisuke
Hironaka, Subanalytic sets, Number theory, algebraic geometry
and commutative algebra, in honor of Yasuo Akizuki, Kinokuniya, Tokyo,
1973, pp. 453–493. MR 0377101
(51 #13275)
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Heisuke
Hironaka, Triangulations of algebraic sets, Algebraic geometry
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1974) Amer. Math. Soc., Providence, R.I., 1975, pp. 165–185.
MR
0374131 (51 #10331)
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Sumner
Byron Myers, Connections between differential geometry and
topology. I. Simply connected surfaces, Duke Math. J.
1 (1935), no. 3, 376–391. MR
1545884, http://dx.doi.org/10.1215/S0012709435001260
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Sumner
Byron Myers, Connections between differential geometry and topology
II. Closed surfaces, Duke Math. J. 2 (1936),
no. 1, 95–102. MR
1545908, http://dx.doi.org/10.1215/S0012709436002089
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Milnor, Morse theory, Based on lecture notes by M. Spivak and
R. Wells. Annals of Mathematics Studies, No. 51, Princeton University
Press, Princeton, N.J., 1963. MR 0163331
(29 #634)
 [6]
M. Buchner, Stability of the cut locus in dimensions (to appear).
 [1]
 H. Hironaka, Subanalytic sets in number theory, algebraic geometry and commutative algebra, Papers in honor of Y. Akizuki, Kinokuniya, Tokyo, 1973, pp. 453493. MR 0377101 (51:13275)
 [2]
 , Triangulations of algebraic sets, Proc. Sympos. Pure Math., vol. 29, Amer. Math. Soc., Providence, R.I., 1975, pp. 165185. 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), 376391. MR 1545884
 [4]
 , Connections between differential geometry and topology. II: Closed surfaces, Duke Math. J. 2 (1936), 95102. 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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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197704741335
PII:
S 00029939(1977)04741335
Article copyright:
© Copyright 1977
American Mathematical Society
