9 citations · 17 across the 9 of their papers we have counts for
11 papers
Normalized Milnor Fibrations for Real Analytic Maps
José Luis Cisneros Molina, Aurélio Menegon
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 fib…
Perplex Analysis and Geometry of Singularities
Aurélio Menegon
We develop a real-analytic framework, called perplex analysis, in which the complex, split-complex, and dual numbers arise as members of a single four-parameter family of two-dimen…
Embedded topological triviality of separable families of singularities
R. Giménez Conejero, Andreas Lind, Aurélio Menegon
Understanding how singularities behave under small perturbations is a central theme in singularity theory. In this paper we establish sufficient conditions for families of analytic…
On deformations of isolated singularity functions
Aurélio Menegon, Miriam da Silva Pereira
We study multi-parameters deformations of isolated singularity function-germs on either a subanalytic set or a complex analytic spaces. We prove that if such a deformation has no c…
Equivalence of Milnor and Milnor-Lê fibrations for real analytic maps
José Luis Cisneros-Molina, Aurélio Menegon
In [22] Milnor proved that a real analytic map , where , with an isolated critical point at the origin has a fibration on the tube $f|\colon…
Fibration theorems à la Milnor for differentiable maps with non-isolated singularities
JosÉ Luis Cisneros-Molina, AurÉlio Menegon, JosÉ Seade +1
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…
Milnor-Lê type fibrations for subanalytic maps
Rafaella de Souza Martins, Aurélio Menegon
We prove a Milnor-Lê type fibration theorem for a subanalytic map between subanalytic sets and . Moreover, if exte…
Vanishing polyhedron and collapsing map
Lê Dũng Tráng, Aurélio Menegon Neto
In this paper we give a detailed proof that the Milnor fiber of an analytic complex isolated singularity function defined on a reduced -equidimensional analytic complex sp…
On the topology of families of isolated singularities
Aurelio Menegon Neto
We study the topology of analytic families of -dimensional complex hypersurfaces having an isolated singularity at the origin. We prove that such a family is -constant if and…
Lê's polyhedron for line singularities
Aurélio Menegon Neto
We study the topology of a line singularity, which is a complex hypersurface with non-isolated singularity given by a complex line. We describe the degeneration of its Milnor fibre…
The boundary of the Milnor fibre of complex and real analytic non-isolated singularities
Javier Fernandez de Bobadilla, Aurelio Menegon Neto
Let f and g be holomorphic function-germs vanishing at the origin of a complex analytic germ of dimension three. Suppose that they have no common irreducible component and that the…