Tohoku Mathematical Journal
2016

September
SECOND SERIES VOL. 68, NO. 3

Tohoku Math. J.
68 (2016), 439-456

Title THE LÊ-GREUEL FORMULA FOR FUNCTIONS ON ANALYTIC SPACES

Author Roberto Callejas-Bedregal, Michelle F. Z. Morgado, Marcelo J. Saia and José Seade

(Received June 17, 2014)
Abstract. In this article we give an extension of the Lê-Greuel formula to the general setting of function germs $(f,g)$ defined on a complex analytic variety $X$ with arbitrary singular set, where $f = (f_1,\ldots,f_k): (X,\underline{0}) \to (\mathbb{C}^k,\underline{0})$ is generically a submersion with respect to some Whitney stratification on $X$. We assume further that the dimension of the zero set $V(f)$ is larger than 0, that $f$ has the Thom $a_f$-property with respect to this stratification, and $g: (X,\underline{0}) \to (\mathbb{C},0)$ has an isolated critical point in the stratified sense, both on $X$ and on $V(f)$.

Mathematics Subject Classification. Primary 32S55; Secondary 14B05, 58K05, 32S05, 57P05.

Key words and phrases. Milnor and Milnor-Lê fibrations, Milnor numbers, Lê-Greuel formula, indices of vector fields, Whitney stratifications.

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