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On the Topology of the Milnor-Lê Fibration for Functions of Three Real Variables

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Abstract

We describe the topology of the local Milnor fiber of a function f defined on a 3-dimensional subanalytic subset \(W \subset {\mathbb {R}}^3\), in terms of the embedded topological type of its link \(K_f\). Precisely, we prove that the interior of the local Milnor fiber of \(\Vert f\Vert \) is homeomorphic to the complement of \(K_f\) in the corresponding sphere, extending a result due to Milnor to non-analytic situations. We also prove that the topology of the fiber does not change if we use a suitable fundamental system of neighborhoods instead of balls, extending to the real setting a classical result due to Lê and Teissier for complex functions.

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Acknowledgements

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  1. Departamento de Matemática, Universidade Federal da Paraíba, João Pessoa, Brazil

    Aurélio Menegon & Camila S. Marques-Silva

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  1. Aurélio Menegon
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  2. Camila S. Marques-Silva
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Correspondence to Aurélio Menegon.

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The second author was supported by CAPES.

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Menegon, A., Marques-Silva, C.S. On the Topology of the Milnor-Lê Fibration for Functions of Three Real Variables. Bull Braz Math Soc, New Series 53, 461–477 (2022). https://doi.org/10.1007/s00574-021-00265-6

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  • DOI: https://doi.org/10.1007/s00574-021-00265-6

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