A parameterized family of tensor products on persistence modules produces Künneth short exact sequences and universal coefficient theorems usable for persistent homology of filtered CW complexes and product spaces.
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3 Pith papers cite this work. Polarity classification is still indexing.
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Defines the walk-length filtration for persistent homology on directed graphs, establishes stability under a generalized L1-style network distance, supplies a computation algorithm, and compares it to the Dowker filtration on cycle and synthetic hippocampal networks.
Three new proofs of Dowker duality are presented using poset fiber lemmas, along with a generalization showing that homologies of simplicial complexes and relational complexes form a long exact sequence.
citing papers explorer
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A continuum of K\"unneth theorems for persistence modules
A parameterized family of tensor products on persistence modules produces Künneth short exact sequences and universal coefficient theorems usable for persistent homology of filtered CW complexes and product spaces.
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The Walk-Length Filtration for Persistent Homology on Weighted Directed Graphs
Defines the walk-length filtration for persistent homology on directed graphs, establishes stability under a generalized L1-style network distance, supplies a computation algorithm, and compares it to the Dowker filtration on cycle and synthetic hippocampal networks.
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Short, new proofs of Dowker duality
Three new proofs of Dowker duality are presented using poset fiber lemmas, along with a generalization showing that homologies of simplicial complexes and relational complexes form a long exact sequence.