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Title

Recognizing right-left equivalence locally

Authors 1

Affiliations

  1. Department of Mathematics, Faculty of Education and Human Sciences, Yokohama National University, Yokohama 240-8501, Japan

Bibliography

  1. V. I. Arnol'd, S. M. Guseĭn-Zade, A. N. Varchenko, Singularities of Differentiable Maps I, Monogr. Math. 82, Birkhäuser, Boston, 1985.
  2. K. Bekka, C-régularité et trivialité topologique, in: Singularity Theory and its Applications (Warwick, 1989), Part I, D. Mond and J. Montaldi (eds.), Lecture Notes in Math. 1462, Springer, Berlin, 1991, 42-62.
  3. M. Fukuda and T. Fukuda, Algebras Q(f) determine the topological types of generic map germs, Invent. Math. 51 (1979), 231-237.
  4. T. Gaffney, A note on the order of determination of a finitely determined germ, Invent. Math. 52 (1979), 127-130.
  5. T. Gaffney, The structure of TA(f), classification and an application to differential geometry, Proc. Sympos. Pure Math. 40 (1983), 409-427.
  6. T. Gaffney and A. A. du Plessis, More on the determinacy of smooth map-germs, Invent. Math. 66 (1982), 137-163.
  7. C. G. Gibson, K. Wirthmüller, A. A. du Plessis, E. J. N. Looijenga, Topological Stability of Smooth Mappings, Lecture Notes in Math. 552, Springer, Berlin, 1976.
  8. J. Martinet, Déploiements versals des applications différentiables et classification des applications stables, in: Singularités d'applications différentiables (Plans-sur-Bex, 1975), O. Burlet, F. Ronga (eds.), Lecture Notes in Math. 535, Springer, Berlin, 1976, 1-44.
  9. J. Mather, Stability of C∞ mappings, III. Finitely determined map-germs, Inst. Hautes Études Sci. Publ. Math. 35 (1968), 127-156.
  10. J. Mather, Stability of C∞ mappings, IV. Classification of stable map-germs by R-algebras, Inst. Hautes Études Sci. Publ. Math. 37 (1969), 223-248.
  11. J. Mather, How to stratify mappings and jet spaces, in: Singularités d'applications différentiables (Plans-sur-Bex, 1975), O. Burlet, F. Ronga (eds.), Lecture Notes in Math. 535, Springer, Berlin, 1976, 128-176.
  12. D. Mond, On the classification of germs of maps from R2 to R3, Proc. London Math. Soc. (3) 50 (1985), 333-369.
  13. T. Nishimura, A constructive method to get right-left equivalence for smooth map germs and its application to divergent diagrams, in: Workshop on Real and Complex Singularities (São Carlos, 1992), M. A. S. Ruas (ed.), Mat. Contemp. 5, Sociedade Brasileira de Matemática, Rio de Janeiro, 1993, 137-160.
  14. T. Nishimura, Isomorphism of smooth map germs with isomorphic local algebras, in: Real Analytic and Algebraic Singularities (Nagoya, 1996), T. Fukuda, T. Fukui, S. Izumiya and S. Koike (eds.), Pitman Res. Notes Math. Ser. 381, Longman, Harlow, 1998, 94-106.
  15. T. Nishimura, Criteria for right-left equivalence of smooth map-germs, preprint, Yokohama National University, 1998.
  16. T. Nishimura, Topological equivalence of K-equivalent map germs, J. London Math. Soc. (2), to appear.
  17. T. Nishimura, Cr K-versality of the graph deformation of a Cr stable map-germ, Math. Proc. Cambridge Philos. Soc., to appear.
  18. T. Nishimura, Topological equivalence of K-equivalent map germs, II, in preparation.
  19. A. A. du Plessis, On the determinacy of smooth map-germs, Invent. Math. 58 (1980), 107-160.
  20. A. A. du Plessis and C. T. C. Wall, The Geometry of Topological Stability, London Math. Soc. Monogr. (N.S.) 9, Oxford University Press, New York, 1995.
  21. C. T. C. Wall, Finite determinacy of smooth map-germs, Bull. London Math. Soc. 13 (1981), 481-539.
Banach Center Publications
1999/50/1
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Pages:
205-215
Main language of publication
English
Published
1999
Exact and natural sciences