106 citations · 247 across the 24 of their papers we have counts for
33 papers
On the additive image of 0th persistent homology
Ulrich Bauer, Magnus Bakke Botnan, Steffen Oppermann +1
For a finite category and a finite field, we study the additive image of the functor $\operatorname{H}_0(-,F) \colon \operatorname{rep}(X, \mathbf{Top}) \to \operatorname{r…
Tropical coefficient dynamics for higher-dimensional cluster categories
Steffen Oppermann, Hugh Thomas
We show that the index in higher-dimensional cluster categories mutates according to a higher-dimensional version of tropical coefficient dynamics.
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…
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…
Partial Serre duality and cocompact objects
Steffen Oppermann, Chrysostomos Psaroudakis, Torkil Stai
A successful theme in the development of triangulated categories has been the study of compact objects. A weak dual notion called 0-cocompact objects was introduced in arXiv:1801.0…
Cotorsion torsion triples and the representation theory of filtered hierarchical clustering
Ulrich Bauer, Magnus B. Botnan, Steffen Oppermann +1
We give a full classification of representation types of the subcategories of representations of an rectangular grid with monomorphisms (dually, epimorphisms) in one o…