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Raimundo N. Araújo dos Santos

Publications and source records attributed to Raimundo N. Araújo dos Santos.

7 recordsLinked to original sources
arXiv2026

Essential tori associated with links of mixed singularities

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 existence of essential tori, topological information, in the complements of links arising from weakly isolated mixed singularities can be detected directly from properties of the defining mixed polynomial, provided that it is convenient, non-degenerate and $Γ$-nice. Our results provide explicit and computable criteria, expressed purely in terms of the polynomial data, that determine the presence of essential tori in the link exterior. In particular, these criteria yield effective conditions ensuring that such links are non-hyperbolic. This approach provides a new method to extract topological information about link complements without requiring an explicit determination of the link type, thereby establishing a concrete bridge between the analytic structure of mixed polynomials and the geometric topology of their associated links.

math.GT↗
arXiv2022

Links of singularities of inner non-degenerate mixed functions

We introduce the notion of a (strongly) inner non-degenerate mixed function $f:\mathbb{C}^2\to\mathbb{C}$. We show that inner non-degenerate mixed polynomials have weakly isolated singularities and strongly inner non-degenerate mixed polynomials have isolated singularities. Furthermore, under one additional assumption, which we call "niceness", the links of these singularities can be completely characterized in terms of the Newton boundary of $f$. In particular, adding terms above the Newton boundary does not affect the topology of the link. This allows us to define an infinite family of real algebraic links in the 3-sphere.

math.GT↗
arXiv2020

Milnor-Hamm sphere fibrations and the equivalence problem

We introduce the sphere fibration for real map germs with radial discriminant and we address the problem of its equivalence with the Milnor-Hamm tube fibration. Under natural conditions, we prove the existence of open book structures with singularities and solve the equivalence problem.

math.AG↗
arXiv2019

Fibrations of highly singular map germs

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 stratified discriminant into the picture. We provide new classes of map germs endowed with such local fibration structures.

math.AG↗
arXiv2014

Real polynomial maps and singular open books at infinity

We provide significant conditions under which we prove the existence of stable open book structures at infinity, i.e. on spheres $S^{m-1}_R$ of large enough radius $R$. We obtain new classes of real polynomial maps $\mathbb R^m \to \mathbb R^p$ which induce such structures.

math.CV↗
arXiv2013

Singular open book structures from real mappings

We prove extensions of Milnor's theorem for germs with nonisolated singularity and use them to find new classes of genuine real analytic mappings $ψ$ with positive dimensional singular locus $\Sing ψ\subset ψ^{-1}(0)$, for which the Milnor fibration exists and yields an open book structure with singular binding.

math.AG↗