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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…