The structure of the cut locus in dimension less than or equal to six

Michael A. Buchner

Compositio Mathematica (1978)

  • Volume: 37, Issue: 1, page 103-119
  • ISSN: 0010-437X

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Buchner, Michael A.. "The structure of the cut locus in dimension less than or equal to six." Compositio Mathematica 37.1 (1978): 103-119. <http://eudml.org/doc/89372>.

@article{Buchner1978,
author = {Buchner, Michael A.},
journal = {Compositio Mathematica},
keywords = {Generic Cut Locus; Compact N-Dimensional Manifolds; Stable Cut Locus; Singularity Theory},
language = {eng},
number = {1},
pages = {103-119},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {The structure of the cut locus in dimension less than or equal to six},
url = {http://eudml.org/doc/89372},
volume = {37},
year = {1978},
}

TY - JOUR
AU - Buchner, Michael A.
TI - The structure of the cut locus in dimension less than or equal to six
JO - Compositio Mathematica
PY - 1978
PB - Sijthoff et Noordhoff International Publishers
VL - 37
IS - 1
SP - 103
EP - 119
LA - eng
KW - Generic Cut Locus; Compact N-Dimensional Manifolds; Stable Cut Locus; Singularity Theory
UR - http://eudml.org/doc/89372
ER -

References

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  1. [1] M. Buchner: Stability of the cut locus in dimensions less than or equal to six. Inventiones Math., 43 (1977) 199-231. Zbl0365.58010MR482816
  2. [2] M. Buchner: Triangulation of the Real Analytic Cut Locus. Proc. of the A.M.S. Vol. 64, No. 1, May 1977. MR474133
  3. [3] J.J. Duistermaat: Oscillatory integrals, Lagrange immersions and unfoldings of singularities. Comm. Pure Appl. Math., vol. XXVII (1974) 207-281. Zbl0285.35010MR405513
  4. [4] J.N. Mather: Stability of C∞ mappings II. Infinitesimal stability implies stability. Ann. of Math. vol. 89 (1969) 254-291. Zbl0177.26002
  5. [5] J.N. Mather: Stability of C∞ mappings, IV; Classification of stable germs by R-algebras. IHES No. 37 (1969) 223-248. Zbl0202.55102
  6. [6] J.N. Mather: Stability of C∞ mappings, V, transversality. Advances in Mathematics, 4 (1970) 301-336. Zbl0207.54303
  7. [7] S.B. Myers: Connections between differential geometry and topology: I. Simply connected surfaces. Duke Math. J., 1 (1935) 376-391. Zbl0012.27502MR1545884JFM61.0787.02
  8. [8] S.B. Myers: Connections between differential geometry and topology: II. Closed surfaces. Duke Math. J., 2 (1936) 95-102. Zbl0013.32201MR1545908JFM62.0861.02
  9. [9] V. Ozols: Cut loci in Riemannian manifolds. Tohoku Math. J. Second Series 26 (1974) 219-227. Zbl0285.53034MR390967
  10. [10] H. Poincaré: Trans. Amer. Math. Soc., 6 (1905) 243. JFM36.0669.01
  11. [11] D. Schaeffer: A regularity theorem for conservation laws. Advances in Mathematics11 (1973) 368-386. Zbl0267.35009MR326178
  12. [12] R. Thom: Temporal evolution of catastrophes in Topology and its Applications, edited by S. Thomeier. Marcel Dekker, Inc.N.Y. Zbl0305.57026MR372925
  13. [13] G. Wasserman: Stability of unfoldings. Lecture Notes in Mathematics393 (1974). Zbl0288.57017MR410789
  14. [14] A. Weinstein: The cut locus and conjugate locus of a Riemannian manifold. Ann. of Math., 87 (1968) 29-41. Zbl0159.23902MR221434
  15. [15] J.H.C. Whitehead: On the covering of a complete space by the geodesics through a point. Ann. of Math., 36 (1935) 679-704. Zbl0012.27802MR1503245
  16. [16] Dubois, Dufour and Stanek: La théorie des catastrophes iv. Déploiments universels et leurs catastrophes. Ann. Inst. Henri Poincaré, Vol. XXIV, No. 3 (1976) 261-300. Zbl0407.58015MR426023
  17. [17] D. Singer, H. Gluck: The existence of nontriangulable cut loci. Bull. Amer. Math. Soc., 82 (1976) 599-602. Zbl0338.53045MR415539

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