43 citations · 149 across the 14 of their papers we have counts for
14 papers
Essential tori associated with links of mixed singularities
Raimundo N. Araújo dos Santos, Benjamin Bode, Thiago de Paiva +1
We establish a direct connection between the analytic data of weakly isolated mixed singularities and the topology of their associated links. More precisely, we prove that the exis…
On the topology of the Milnor Boundary for real analytic singularities
R. Araújo dos Santos, A. Menegon, M. Ribeiro +2
We study the topology of the boundaries of the Milnor fibers of real analytics map-germs and $f_{I}:=Π_{I}\circ f : (\mathbb{R}^M,0) \to…
Tameness conditions and the Milnor fibrations for composite singularities
R. N. Araújo dos Santos, D. Dreibelbis, M. F. Ribeiro +1
In this paper, we introduce a new regularity condition that characterizes the tameness of a composite singularity in a sharp way. Our approach provides a natural tool…
Links of singularities of inner non-degenerate mixed functions
Raimundo N. Araújo dos Santos, Benjamin Bode, Eder L. Sanchez Quiceno
We introduce the notion of a (strongly) inner non-degenerate mixed function . We show that inner non-degenerate mixed polynomials have weakly isolated…
On real algebraic links in the 3-sphere associated with mixed polynomials
Raimundo N. Aráujo dos Santos, Eder L. Sanchez Quiceno
In this paper we construct new classes of mixed singularities that provide realizations of real algebraic links in the -sphere. Classifications and characterizations of real alg…
Fibrations of highly singular map germs
Maico F. Ribeiro, Raimundo N. Araújo dos Santos, Mihai Tibăr
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…
Fibrations structure and degree formulae for Milnor fibers
Nicolas Dutertre, Raimundo N. Araújo Dos Santos, Ying Chen +1
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 gi…
Open book structures on semi-algebraic manifolds
Nicolas Dutertre, Raimundo N. Araújo Dos Santos, Ying Chen +1
Given a semi-algebraic mapping we consider its restriction to an embedded closed semi-algebraic…
New examples of Neuwirth-Stallings pairs and non-trivial real Milnor fibrations
R. Araújo Dos Santos, M. A. B. Hohlenwerger, O. Saeki +1
We use topology of configuration spaces to give a characterization of Neuwirth--Stallings pairs with . As a consequence, we construct polynomial map germs $(…
Real polynomial maps and singular open books at infinity
Raimundo N. Araújo dos Santos, Ying Chen, Mihai Tibar
We provide significant conditions under which we prove the existence of stable open book structures at infinity, i.e. on spheres of large enough radius . We obtain n…
Characterizations of trivial maps in 3-dimensional real Milnor fibers
Tacina O. Souza, Maria A. P. Hohlenwerger, Denise De Mattos +1
In this paper we extend the characterization of trivial map-germs for the real Milnor fibrations started by Church and Lamotke. Our main result cover all cases on the three dimensi…
Singular open book structures from real mappings
Mihai Tibar, Ying Chen, Raimundo N. Araújo dos Santos
We prove extensions of Milnor's theorem for germs with nonisolated singularity and use them to find new classes of genuine real analytic mappings with positive dimensional sing…
Equivalence of real Milnor's fibrations for quasi homogeneous singularities
R. Araujo dos Santos
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" hollow…
Real map germs and higher open books
Raimundo Araújo dos Santos, Mihai Tibăr
We present a general criterion for the existence of open book structures defined by real map germs $(\bR^m, 0) \to (\bR^p, 0)$, where , with isolated critical point. We…