Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-23T14:29:27.606Z Has data issue: false hasContentIssue false
  • English
  • Français

Geometry of singular sets

Published online by Cambridge University Press:  24 October 2008

J. W. Bruce
J. W. Bruce
Affiliation:
Department of Pure Mathematics, The University, Newcastle upon Tyne NE1 7RU
Get access Rights & Permissions [Opens in a new window]

Extract

Singularity theory is concerned with the study of smooth mappings between smooth manifolds. Given two such manifolds X and Y and a pair of smooth mappings f1,f2: X→Y we say that f1 and f2 are -equivalent if there are diffeomorphisms α: X→X and β: Y→Y with βof1oα = f2. Clearly -equivalence is an equivalence relation, and one aims to classify smooth mappings f: X→Y up to this equivalence.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 3 , November 1989 , pp. 495 - 509
Copyright
Copyright © Cambridge Philosophical Society 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Arnol'd, V. I.. Wavefront evolution and equivariant Morse lemma. Comm. Pure Appl. Math. 29 (1976), 557–582.CrossRefGoogle Scholar
[2]Arnol'd, V. I.. Catastrophe Theory (Springer-Verlag, 1984).CrossRefGoogle Scholar
[3]Arnol'd, V. I., Gusein-Zade, S. M. and Varchenko, A. N.. Singularities of Differentiable Maps, vol. I (Birkhauser, 1985).CrossRefGoogle Scholar
[4]Banchoff, T., Gaffney, T. J. and McCrory, C.. Cusps of Gauss Mappings. Research Notes in Mathematics no. 55 (Pitman, 1982).Google Scholar
[5]Bruce, J. W.. The duals of generic hypersurfaces. Math. Scand. 49(1981), 36–60.CrossRefGoogle Scholar
[6]Bruce, J. W.. Wavefronts and parallels in Euclidean space. Math. Proc. Cambridge Philos. Soc. 93 (1983), 323–333.CrossRefGoogle Scholar
[7]Bruce, J. W. and Giblin, P. J.. Outlines and their duals. Proc. London Math. Soc. (3) 50 (1985). 552–570.CrossRefGoogle Scholar
[8]Bruce, J. W. and Giblin, P. J.. Smooth stable maps of discriminant varieties. Proc. London Math. Soc. (3) 50 (1985). 535–551.CrossRefGoogle Scholar
[9]Gaffney, T. J.. The structure of T (f), classification and an application to differential geometry. In Singularities, Proceedings of Symposia in Pure Mathematics, no. 40 (American Mathematical Society, 1983). pp. 429–438.CrossRefGoogle Scholar
[10]Gibson, C. G.. Wirthmuller, K., Plessis, A. A. Du and Looijenga, E. J. N.. Topological Stability of Smooth Mappings. Lecture Notes in Math. vol. 552 (Springer-Verlag, 1976).CrossRefGoogle Scholar
[11]Golubitsky, M. and Guillemin, V.. Stable Mappings and their Singularities. Graduate Texts in Math. no. 14 (Springer-Verlag. 1973).CrossRefGoogle Scholar
[12]McCrory, C.. Profiles of surfaces. (Preprint, University of Warwick, 1980; corrected 1981.)Google Scholar
[13]Mond, D. M. Q.. Some remarks on the geometry and classification of germs of maps from surfaces to 3-space. Topology 26 (1987), 361–383.CrossRefGoogle Scholar
[14]Montaldi, J.. On contact between submanifolds. Michigan Math. J. 33 (1986), 195–199.CrossRefGoogle Scholar
[15]Plessis, A. Du and Wilson, L.. On right-equivalence. Math. Z. 190 (1985), 163–205.CrossRefGoogle Scholar
[16]Wall, C. T. C.. Finite determinacy of smooth map-germs. Bull. London Math. Soc. 13 (1981), 481–539.CrossRefGoogle Scholar