3 papers
math.AC2026
Dualities in Multiparameter Persistence
Ulrich Bauer, Fabian Lenzen, Michael Lesnick
In the theory of persistent homology, a well known duality relates the barcodes of the absolute homology and relative cohomology of a one-parameter simplicial filtration. Motivated…
math.RT2025
Multi-Parameter Persistence Modules are Generically Indecomposable
Ulrich Bauer, Luis Scoccola
Algebraic persistence studies persistence modules (typically, linear representations of the poset with ) and the algebraic relationships between persistenc…
math.AT2025
A Unified View on the Functorial Nerve Theorem and its Variations
Ulrich Bauer, Michael Kerber, Fabian Roll +1
The nerve theorem is a basic result of algebraic topology that plays a central role in computational and applied aspects of the subject. In topological data analysis, one often nee…