TOPOLOGICAL INVARIANTS AND MILNOR FIBER FOR A-FINITE GERMS C^2 → C^3

Authors

  • Javier Fernández de Bobadilla Basque Foundation for Science, Spain
  • Guillermo Peñafort-Sanchis Mazarredo, Bilbao, Spain
  • José Edson Sampaio Universidade Federal do Ceará, Rua Campus do Pici, Brazil

DOI:

https://doi.org/10.37569/DalatUniversity.12.2.864(2022)

Keywords:

Milnor fiber, Topological invariance.

Abstract

This note is the observation that a simple combination of known results shows that the usual analytic invariants of a finitely determined multi-germ f : (C^2 , S) → (C^3 , 0) —namely, the image Milnor number , the number of cross-caps and triple points, C and T, and the Milnor number μ(Σ) of the curve of double points in the target—depend only on the embedded topological type of the image of f. As a consequence, one obtains the topological invariance of the sign-refined Smale invariant for immersions j : S^3 → S^5 associated to finitely determined map germs (C^2 , 0) → (C^3 , 0).

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References

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Published

28-01-2022

Volume and Issues

Section

Natural Sciences and Technology

How to Cite

Fernández De Bobadilla, J., Peñafort-Sanchis, G., & Sampaio, J. E. (2022). TOPOLOGICAL INVARIANTS AND MILNOR FIBER FOR A-FINITE GERMS C^2 → C^3. Dalat University Journal of Science, 12(2), 19-25. https://doi.org/10.37569/DalatUniversity.12.2.864(2022)