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.