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Tohoku Mathematical Journal
2016
September
SECOND SERIES VOL. 68, NO. 3
Tohoku Math. J.
68 (2016), 439456

Title
THE LÊGREUEL FORMULA FOR FUNCTIONS ON ANALYTIC SPACES
Author
Roberto CallejasBedregal, Michelle F. Z. Morgado, Marcelo J. Saia and José Seade
(Received June 17, 2014) 
Abstract.
In this article we give an extension of the LêGreuel 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 MilnorLê fibrations, Milnor numbers, LêGreuel formula, indices of vector fields, Whitney stratifications.


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