Notes on C0 sufficiency of quasijets

Satoshi KOIKE

doi:10.2969/jmsj/04220265

Notes on C⁰ sufficiency of quasijets

Satoshi KOIKE

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JOURNAL FREE ACCESS

1990 Volume 42 Issue 2 Pages 265-275

DOI https://doi.org/10.2969/jmsj/04220265

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Published: 1990 Received: August 15, 1988 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: DTRECEIVED Details: Wrong : 19880415
Right : 19880815

Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Masahisa Adachi on his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) V. I. Arnol'd, Normal forms of functions in the neighborhood of degenerate critical points, Uspekhi Mat. Nauk, 29 (1974), 11-49=Russian Math. Surveys, 29 (1974), 19-48.
2) J. Bochnak and J.-J. Risler, Sur les exposants de Lojasiewicz, Comment. Math. Helv., 50 (1975), 493-507.
3) M. Buchner and W. Kucharz, Topological triviality of a family of zero-sets, Proc. Amer. Math. Soc., 102 (1988), 699-705.
4) J. Damon and T. Gaffney, Topological triviality of deformations of functions and Newton filtrations, Invent. Math., 72 (1983), 335-358.
5) H. King, Topological type in families of germs, Invent. Math., 62 (1980), 1-13.
6) S. Koike, C⁰-sufficiency of jets via blowing-up, J. Math. Kyoto Univ., 28 (1988), 605-614.
7) S. Koike, A partition problem on analytic functions, Singularities and Differential Geometry, Hokkaido University Technical Report Series in Math., 7 (1988).
8) A. G. Kouchnirenko, Polyhèdres de Newton et nombres de Milnor, Invent. Math., 32 (1976), 1-31.
9) N. Kuiper, C¹-equivalence of functions near isolated critical points, Symposium on Infinite Dimensional Topology (Baton Rouge 1967), Ann. of Math. Stud., 69 (1972), 199-218.
10) T. C. Kuo, On C⁰-sufficiency of jets of potential functions, Topology, 8 (1969), 167-171.
11) T. C. Kuo, Characterizations of v-sufficiency of jets, Topology, 11 (1972), 115-131.
12) T. C. Kuo, Computation of Lojasiewicz exponent of f(x, y), Comment. Math. Helv., 49 (1974), 201-213.
13) J. Mather, Notes on topological stability, Harvard University notes, 1970.
14) J. Milnor, Singular points of complex hypersurfaces, Ann. of Math. Stud., 61, 1968.
15) M. Oka, On the bifurcation of the multiplicity and topology of the Newton boundary, J. Math. Soc. Japan, 31 (1979), 435-450.
16) M. Suzuki, The stratum with constant Milnor number of a mini-transversal family of a quasihomogeneous function of corank two, Topology, 23 (1983), 101-115.
17) J. Timourian, The invariance of Milnor's number implies topological triviality, Amer. J. Math., 99 (1977), 437-446.
18) A. N. Varcenko, A lower bound for the codimension of the stratum μ=const in terms of the mixed Hodge structure, Vestnik Moskov. Univ., 37 (1982), 28-31.
19) E. Yoshinaga, The modified analytic trivialization of real analytic families via blowing-ups, J. Math. Soc. Japan, 40 (1988), 161-179.

Right : [1] V. I. Arnol'd, Normal forms of functions in the neighborhood of degenerate critical points, Uspekhi Mat. Nauk, 29 (1974), 11-49=Russian Math. Surveys, 29 (1974), 19-48.
[2] J. Bochnak and J. -J. Risler, Sur les exposants de Lojasiewicz, Comment. Math. Helv., 50 (1975), 493-507.
[3] M. Buchner and W. Kucharz, Topological triviality of a family of zero-sets, Proc. Amer. Math. Soc., 102 (1988), 699-705.
[4] J. Damon and T. Gaffney, Topological triviality of deformations of functions and Newton filtrations, Invent. Math., 72 (1983), 335-358.
[5] H. King, Topological type in families of germs, Invent. Math., 62 (1980), 1-13.
[6] S. Koike, C⁰-sufficiency of jets via blowing-up, J. Math. Kyoto Univ., 28 (1988), 605-614.
[7] S. Koike, A partition problem on analytic functions, Singularities and Differential Geometry, Hokkaido University Technical Report Series in Math., 7 (1988).
[8] A. G. Kouchnirenko, Polyhèdres de Newton et nombres de Milnor, Invent. Math., 32 (1976), 1-31.
[9] N. Kuiper, C¹-equivalence of functions near isolated critical points, Symposium on Infinite Dimensional Topology (Baton Rouge 1967), Ann. of Math. Stud., 69 (1972), 199-218.
[10] T. C. Kuo, On C⁰-sufficiency of jets of potential functions, Topology, 8 (1969), 167-171.
[11] T. C. Kuo, Characterizations of v-sufficiency of jets, Topology, 11 (1972), 115-131.
[12] T. C. Kuo, Computation of Lojasiewicz exponent of f(x, y), Comment. Math. Helv., 49 (1974), 201-213.
[13] J. Mather, Notes on topological stability, Harvard University notes, 1970.
[14] J. Milnor, Singular points of complex hypersurfaces, Ann. of Math. Stud., 61, 1968.
[15] M. Oka, On the bifurcation of the multiplicity and topology of the Newton boundary, J. Math. Soc. Japan, 31 (1979), 435-450.
[16] M. Suzuki, The stratum with constant Milnor number of a mini-transversal family of a quasihomogeneous function of corank two, Topology, 23 (1983), 101-115.
[17] J. Timourian, The invariance of Milnor's number implies topological triviality, Amer. J. Math., 99 (1977), 437-446.
[18] A. N. Varcenko, A lower bound for the codimension of the stratum μ=const in terms of the mixed Hodge structure, Vestnik Moskov. Univ., 37 (1982), 28-31.
[19] E. Yoshinaga, The modified analytic trivialization of real analytic families via blowing-ups, J. Math. Soc. Japan, 40 (1988), 161-179.

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