Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-01T07:11:53.940Z Has data issue: false hasContentIssue false
  • English
  • Français

Homotopy type of disentanglements of multi-germs

Published online by Cambridge University Press:  01 September 2009

KEVIN HOUSTON
KEVIN HOUSTON*
Affiliation:
School of Mathematics, University of Leeds, Leeds, LS2 9JT. e-mail: k.houston@leeds.ac.uk. http://www.maths.leeds.ac.uk/~khouston/
Get access Rights & Permissions [Opens in a new window]

Abstract

For a complex analytic map f from n-space to p-space with n < p and with an isolated instability at the origin, the disentanglement of f is a local stabilization of f that is analogous to the Milnor fibre for functions.

For mono-germs it is known that the disentanglement is a wedge of spheres of possibly varying dimensions. In this paper we give a condition that allows us to deduce that the same is true for a large class of multi-germs.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 147 , Issue 2 , September 2009 , pp. 505 - 512
Copyright
Copyright © Cambridge Philosophical Society 2009

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]Damon, J. and Mond, D.A-codimension and vanishing topology of discriminants. Invent. Math. 106 (1991), 217–242.CrossRefGoogle Scholar
[2]Goryunov, V. V.Semi-simplicial resolutions and homology of images and discriminants of mappings. Proc. London Math. Soc. 70 (1995), 363–385.CrossRefGoogle Scholar
[3]Houston, K.Local topology of images of finite complex analytic maps. Topology 36 (1997), 1077–1121.CrossRefGoogle Scholar
[4]Houston, K. A general image computing spectral sequence. Singularity Theory, ed., Chéniot, Denis, Dutertre, Nicolas, Murolo, Claudio, Trotman, David and Pichon, Anne (World Scientific Publishing, 2007), 651–675.CrossRefGoogle Scholar
[5]Houston, K. Stratification of unfoldings of corank 1 singularities. To appear in Quart. J. Math. doi:10.1093/qmath/hap012.CrossRefGoogle Scholar
[6]Marar, W. L.Mapping fibrations. Manuscripta Math. 80 (1993), 273–281.CrossRefGoogle Scholar
[7]Mond, D. Vanishing cycles for analytic maps. in Singularity Theory and its Applications, SLNM 1462. Mond, D., Montaldi, J. (eds.) (Springer Verlag, 1991), 221–234.CrossRefGoogle Scholar
[8]Switzer, R. M.Algebraic Topology – Homology and Homotopy. Reprint of the 1975 original, Classics in Mathematics (Springer-Verlag, 2002).Google Scholar