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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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