Generalizations of persistent homology
Date
2021
Authors
McCleary, Alexander J., author
Patel, Amit, advisor
Adams, Henry, committee member
Ben Hur, Asa, committee member
Peterson, Chris, committee member
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Abstract
Persistent homology typically starts with a filtered chain complex and produces an invariant called the persistence diagram. This invariant summarizes where holes are born and die in the filtration. In the traditional setting the filtered chain complex is a chain complex of vector spaces filtered over a totally ordered set. There are two natural directions to generalize the persistence diagram: we can consider filtrations of more general chain complexes and filtrations over more general partially ordered sets. In this dissertation we develop both of these generalizations by defining persistence diagrams for chain complexes in an essentially small abelian category filtered over any finite lattice.
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Subject
persistent homology
applied topology