On Real Singularities with a Milnor Fibration

2002 ◽  
pp. 191-213 ◽  
Author(s):  
Maria Aparecida Soares Ruas ◽  
José Seade ◽  
Alberto Verjovsky
Keyword(s):  
Milnor Fibration ◽  
Real Singularities

Open-book decompositions of 𝕊5 and real singularities

2014 ◽  
Vol 25 (09) ◽  
pp. 1450085
Author(s):  
Haydée Aguilar-Cabrera
Keyword(s):  
Open Book ◽  
Isolated Singularity ◽  
Complex Singularity ◽  
Seifert Manifold ◽  
Milnor Fibration ◽  
Open Book Decompositions ◽  
The Family ◽  
Real Analytic ◽  
Almost All ◽  
Real Singularities

In this article, we study the topology of the family of real analytic germs F : (ℂ3, 0) → (ℂ, 0) given by [Formula: see text] with p, q, r ∈ ℕ, p, q, r ≥ 2 and (p, q) = 1. Such a germ has an isolated singularity at 0 and gives rise to a Milnor fibration [Formula: see text]. Moreover, it is known that the link LF is a Seifert manifold and that it is always homeomorphic to the link of a complex singularity. However, we prove that in almost all the cases the open-book decomposition of 𝕊5 given by the Milnor fibration of F cannot come from the Milnor fibration of a complex singularity in ℂ3.

The real singularities of theN-body problem in celestial mechanics

1970 ◽  
Vol 2 (3) ◽  
pp. 355-357 ◽  
Author(s):  
Hans J. Sperling
Keyword(s):  
Celestial Mechanics ◽  
Body Problem ◽  
The Real ◽  
Real Singularities

scholarly journals On the Lê-Milnor fibration for real analytic maps

2016 ◽  
Vol 290 (2-3) ◽  
pp. 382-392 ◽  
Author(s):  
Aurélio Menegon Neto ◽  
José Seade
Keyword(s):  
Milnor Fibration ◽  
Real Analytic ◽  
Analytic Maps

MILNOR FIBRATIONS AND d-REGULARITY FOR REAL ANALYTIC SINGULARITIES

2010 ◽  
Vol 21 (04) ◽  
pp. 419-434 ◽  
Author(s):  
J. L. CISNEROS-MOLINA ◽  
J. SEADE ◽  
J. SNOUSSI
Keyword(s):  
Fiber Bundle ◽  
Critical Value ◽  
Singular Set ◽  
Small Sphere ◽  
Milnor Fibration ◽  
Analytic Varieties ◽  
Real Analytic ◽  
Analytic Singularities ◽  
Analytic Maps ◽  
Do So

We study Milnor fibrations of real analytic maps [Formula: see text], n ≥ p, with an isolated critical value. We do so by looking at a pencil associated canonically to every such map, with axis V = f-1(0). The elements of this pencil are all analytic varieties with singular set contained in V. We introduce the concept of d-regularity, which means that away from the axis each element of the pencil is transverse to all sufficiently small spheres. We show that if V has dimension 0, or if f has the Thom af-property, then f is d-regular if and only if it has a Milnor fibration on every sufficiently small sphere, with projection map f/‖f‖. Our results include the case when f has an isolated critical point. Furthermore, we show that if f is d-regular, then its Milnor fibration on the sphere is equivalent to its fibration on a Milnor tube. To prove these fibration theorems we introduce the spherefication map, which is rather useful to study Milnor fibrations. It is defined away from V; one of its main properties is that it is a submersion if and only if f is d-regular. Here restricted to each sphere in ℝn the spherefication gives a fiber bundle equivalent to the Milnor fibration.

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