Invariants for Tame Parametrised Chain Complexes

Explore invariants for tame parametrized chain complexes in this lecture from the Applied Algebraic Topology Network. Delve into the construction of new and existing invariants derived from model structures for persistent chain complexes, and discover their applications in Topological Data Analysis (TDA). Learn about explicit constructions with computable methods, a comprehensive framework encompassing various persistence theories, and the discriminative power of persistent chain complex invariants. Gain insights into minimal factorization, chain complexes over fields, and the characterization of cofibrant objects. Examine the construction of minimal covers, indecomposable cofibrant objects, and information on the diagonal. Investigate the completeness of minimal covers, explore other invariants, and understand the new persistence pipeline. Review a papers database of TDA real-world applications and analyze an example of the persistence diagram of a minimal cover.

Intro
Minimal factorisation
Chain complexes over a field
Examples of tame parametrised chain complexes
Construction of minimal covers
Characterisation of cofibrant objects
Indecomposable cofibrant objects
Information on the diagonal
Completeness of the minimal cover
Other invariants
New Persistence pipeline
Papers database of TDA real-world applications
PD of a minimal cover: example (2)