2 papers
math.AT2024
On the bottleneck stability of rank decompositions of multi-parameter persistence modules
Magnus Bakke Botnan, Steffen Oppermann, Steve Oudot +1
A significant part of modern topological data analysis is concerned with the design and study of algebraic invariants of poset representations -- often referred to as multi-paramet…
math.AT2024
Signed Barcodes for Multi-Parameter Persistence via Rank Decompositions and Rank-Exact Resolutions
Magnus Bakke Botnan, Steffen Oppermann, Steve Oudot
In this paper, we introduce the signed barcode, a new visual representation of the global structure of the rank invariant of a multi-parameter persistence module or, more generally…