Geodesic
Milnor Fibrations and the Thom Property for maps fḡ
Journal of Singularities, Tome 3 (2011), pp. 144-150

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We prove that every map-germ fḡ: (C^n, 0) →(C, 0) with an isolated critical value at 0 has the Thom a_{fḡ}-property. This extends Hironaka's theorem for holomorphic mappings to the case of map-germs fḡ and it implies that every such map-germ has a Milnor-Lê fibration defined on a Milnor tube. One thus has a locally trivial fibration φ: S_ε – K → S^1 for every sufficiently small sphere around 0, where K is the link of fḡ and in a neighbourhood of K the projection map φ is given by fḡ/ | fḡ|.
DOI : 10.5427/jsing.2011.3i
Classification : :32S55, 32C05, 57Q45. 
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     author = {Anne Pichon and Jos\'e Seade},
     title = {Milnor {Fibrations} and the {Thom} {Property} for maps fḡ},
     journal = {Journal of Singularities},
     pages = {144--150},
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Anne Pichon; José Seade. Milnor Fibrations and the Thom Property for maps fḡ. Journal of Singularities, Tome 3 (2011), pp. 144-150. doi: 10.5427/jsing.2011.3i

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