3 papers
math.CV2026
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…
math.CV2025
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…
math.AG2025
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…