Fibration theorems à la Milnor for differentiable maps with non-isolated singularities

2020/02/17 by Cisneros-Molina, JosÉ Luis, Menegon, AurÉlio, Seade, JosÉ +1
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.07120

Abstract

We prove fibration theorems à la Milnor for differentiable real maps with non isolated critical values. We study the situation for maps with linear discriminant, and prove that the concept of d-regularity is the key point for the existence of a Milnor fibration on the sphere. We also explain how one can modify the target space by homeomorphisms to linearize a general discriminant. Whenever the composed map is d-regular one has fibration on the sphere. Plenty of examples are discussed along the text.

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