Dualities in persistent (co)homology

Details Dualities in persistent (co)homology Dualities in persistent (co)homology

2011-07-28

arxiv.org/abs/1107.5665v1

Mathematics

Algebraic Topology

16 pages, 3 figures, submitted to the Inverse Problems special issue on Topological Data Analysis

Scientific paper

We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their persistence modules, and show that they contain equivalent information. We explain how one can use the existing algorithm for persistent homology to process any of the four modules, and relate it to a recently introduced persistent cohomology algorithm. We present experimental evidence for the practical efficiency of the latter algorithm.

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