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