Directed Homology and Persistence Modules
Eric Goubault
TL;DR
This paper introduces a directed homology theory based on modules over algebras, connecting it to persistence and natural homology, and explores its fundamental properties including exact sequences.
Contribution
It presents a new algebraic framework for directed homology, bridging it with existing homology theories and analyzing its initial properties.
Findings
Establishment of a directed homology construction from algebra modules
Connection between directed homology, persistence homology, and natural homology
Initial properties including exact sequences of the new theory
Abstract
In this note, we give a self-contained account on a construction for a directed homology theory based on modules over algebras, linking it to both persistence homology and natural homology. We study its first properties, among which some exact sequences.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models