Biparametric persistence for smooth filtrations

Abstract

The goal of this note is to define biparametric persistence diagrams for smooth generic mappings $h=(f,g):M\to V\cong {\mathbb{R}}^2$ for smooth compact manifold $M$. Existing approaches to multivariate persistence are mostly centered on the workaround of absence of reasonable algebraic theories for quiver representations for lattices of rank 2 or higher, or similar artificial obstacles. We approach the problem from the Whitney theory perspective, similar to how single parameter persistence can be viewed through the lens of Morse theory.

References in corpus (1)

• Data structures for real multiparameter persistence modules