Geodesic
Topological invariants of germs of real analytic functions
Glasgow mathematical journal, Tome 39 (1997) no. 1, pp. 85-89

Voir la notice de l'article provenant de la source Cambridge University Press

Let f: (Rn, 0)→ (R,0) be a germ of a real analytic function. Let L and F(f) denote the link of f and the Milnor fibre of fc respectively, i. e., L = {x ∈ Sn−1 | f(x) = 0}, , where 0 ≤ ξ ≪ r ≪ 1, . In [2] Szafraniec introduced the notion of an -germ as a generalization of a germ defined by a weighted homogeneous polynomial satisfying some condition concerning the relation between its degree and weights (definition 1). He also proved that if f is an -germ (presumably with nonisolated singularity) then the number χ(F(f)/d mod 2 is a topological invariant of f, where χ(F(f)) is the Euler characterististic of F(f), and gave the formula for χ(L)/2 mod 2 (it is a well-known fact that F(L) is an even number). As a simple consequence he got the fact that χ(F(f)mod 2 is a topological invariant for any f, which is a generalization of Wall's result [3] (he considered only germs with an isolated singularity). 
Dudziński, Piotr. Topological invariants of germs of real analytic functions. Glasgow mathematical journal, Tome 39 (1997) no. 1, pp. 85-89. doi: 10.1017/S0017089500031943
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[1] 1.Milnor, J., Singular points of complex hypersurfaces (Princeton University Press 1968). Google Scholar

[2] 2.Szafraniec, Z., On the topological invariants of germs of analytic functions Topology 26 (1987), 235–238. Google Scholar

[3] 3.Wall, C. T. C., Topological invariance of the Milnor number mod 2, Topology 22 (1983), 345–350. Google Scholar

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