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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Saeki, Osamu and Yamamoto, Takahiro 2006. Singular fibers of stable maps and signatures of 4–manifolds. Geometry & Topology, Vol. 10, Issue. 1, p. 359.


    Gaffney, Terence 1993. Polar multiplicities and equisingularity of map germs. Topology, Vol. 32, Issue. 1, p. 185.


    Wall, C.T.C. 1990. Deformations of real singularities. Topology, Vol. 29, Issue. 4, p. 441.


    Wall, C.T.C. 1983. Topological invariance of the milnor number mod 2. Topology, Vol. 22, Issue. 3, p. 345.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 89, Issue 3
  • May 1981, pp. 457-472

Topological properties of real simple germs, curves, and the nice dimensions n > p

  • James Damon (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100058369
  • Published online: 24 October 2008
Abstract

Infinitesimally stable germs play an important role both as germs from which global C-stable mappings are constructed and as germs representing versal unfoldings of (C or holomorphic) germs. Because of the presence of moduli, the C (or analytic) classification of these germs is insufficient and the topological classification of these germs must be understood as well. Here we consider the classification of such germs in the region where no moduli occur. This region is important for several reasons. Most importantly, it contains the infinitesimally stable germs occurring in the nice dimensions. These are the dimensions in which globally infinitesimally stable mappings are dense among the proper C-mappings. In (4), it was proved that the topological and C-classifications agree for infinitesimally stable germs f: n, 0 → p, 0 in the nice dimensions, np. This was then used in (5) to characterize those topologically stable germs which are C-stable.

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(3)J. Callahan Singularities and plane maps. II. Sketching catastrophes. Amer. Math. Monthly 84 (1977), 765803.

(8)E. Looijenga On the semi-universal deformation of a simple elliptic hypersurface singularity. I: Unimodularity. Topology 16 (1977), 257262. II: The discriminant. Topology 17 (1978), 23–40.

(9)J. Mather Stability of C∞-mappings. III: Finitely determined map germs. Publ. I.H.E.S. 35 (1968), 127156. IV: Classification of stable germs by R-algebras. Publ. I.H.E.S. 37 (1969), 237–248. VI: The nice dimensions. Liverpool Singularities Symposium. Springer Lecture Notes, no. 192 (1971), pp. 207–253.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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