Flat covers and injective hulls of persistence modules
Eero Hyry, Ville Puuska
TL;DR
This paper establishes a duality between flat covers and injective hulls of persistence modules, extending the theory to non-tame modules using flat cotorsion modules, advancing topological data analysis tools.
Contribution
It introduces a Matlis duality framework for persistence modules, broadening applicability to non-tame modules in topological data analysis.
Findings
Duality between minimal flat and injective resolutions
Extension of flat cover theory to non-tame modules
Application of cotorsion modules in persistence theory
Abstract
Motivated by recent progress in topological data analysis, we establish a Matlis duality between injective hulls and flat covers of persistence modules. This extends to a duality between minimal flat and minimal injective resolutions. We utilize the theory of flat cotorsion modules and flat covers developed by Enochs and Xu. By means of this theory we can work with persistence modules which are not tame or even pointwise finite-dimensional.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology