Related papers: Milnor-Hamm sphere fibrations and the equivalence …
We prove fibration theorems \`a 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…
We find natural and convenient conditions which allow us to produce classes of genuine real map germs with Milnor tube fibration, either with Thom regularity or without it.
We introduce several sufficient conditions to guarantee the existence of the Milnor vector field for new classes of singularities of map germs. This special vector field is related with the equivalence problem of the Milnor fibrations for…
We prove extensions of Milnor's theorem for germs with nonisolated singularity and use them to find new classes of genuine real analytic mappings $\psi$ with positive dimensional singular locus $\Sing \psi \subset \psi^{-1}(0)$, for which…
Milnor's fibration theorem and its generalizations play a central role in the study of singularities of complex and real analytic maps. In the complex analytic case, the Milnor fibration on the sphere is always given by the normalized map…
In the present article we determine and characterize completely the support genus, the binding number and the norm of a page of an open book under the following restrictions: M is a rational homology sphere which can be realized as the link…
We define local fibration structures for real map germs with strictly positive dimensional discriminant: a local fibration structure over the complement of the discriminant, and a complete local fibration structure which includes the…
In this paper we present new results about the topology of the Milnor fibrations of analytic function-germs with a special attention to the topology of the fibers. In particular, we provide a short review on the existence of the Milnor…
We discuss the most general condition under which a singular local tube fibration exists. We give an application to composition of map germs.
In this paper we study the Milnor fibrations associated to real analytic map germs $\psi:(\mathbb{R}^{m},0) \to (\mathbb{R}^2,0)$ with isolated critical point at $0\in \mathbb{R}^{m}$. The main result relates the existence of called Strong…
In analogy with the holomorphic case, we compare the topology of Milnor fibrations associated to a meromorphic germ f/g : the local Milnor fibrations given on Milnor tubes over punctured discs around the critical values of f/g, and the…
In this paper, we discuss the concept of $\rho$-regularity of analytic map germs and its close relationship with the existence of locally trivial smooth fibrations, known as the Milnor fibrations. The presence of a Thom regular…
In [22] Milnor proved that a real analytic map $f\colon (R^n,0) \to (R^p,0)$, where $n \geq p$, with an isolated critical point at the origin has a fibration on the tube $f|\colon B_\epsilon^n \cap f^{-1}(S_\delta^{p-1}) \to…
When f : R power n to R power p, is a surjective real analytic map with isolated critical value, we prove that the (m)-regularity condition (in a sense we define) ensures that f ||f|| is a fibration on small spheres, f induces a fibration…
We are going to use the Euler's vector fields in order to show that for real quasi-homogeneous singularities with isolated critical value, the Milnor's fibration in a "thin" hollowed tube involving the zero level and the fibration in the…
In this article, we study the topology of real analytic germs $F \colon (\C^3,0) \to (\C,0)$ given by $F(x,y,z)=\overline{xy}(x^p+y^q)+z^r$ with $p,q,r \in \N$, $p,q,r \geq 2$ and $(p,q)=1$. Such a germ gives rise to a Milnor fibration…
We describe a new algebro-geometric perspective on the study of the Milnor fibration and, as a first step toward putting it into practice, prove powerful criteria for a deformation of a holomorphic function germ to admit a stratification on…
In this survey, we remind some fibrations structure theorems (also called Milnor's fibrations) recently proved in the real and complex case, in the local and global settings. We give several Poincar\'e-Hopf type formulae which relates the…
In this paper, we study the topology of real analytic map-germs with isolated critical value $f: (\mathbb{R}^m,0) \to (\mathbb{R}^n,0)$, with $1 <n <m$. We compare the topology of $f$ with the topology of the compositions $\pi_i^* \circ f$,…
Given a $C^2$ semi-algebraic mapping $F: \mathbb{R}^N \rightarrow \mathbb{R}^p,$ we consider its restriction to $W\hookrightarrow \mathbb{R^{N}}$ an embedded closed semi-algebraic manifold of dimension $n-1\geq p\geq 2$ and introduce…