2011/07/28 by Vin de Silva, Dmitriy Morozov, Mikael Vejdemo-Johansson · 2 citations
Mathematics · Computer Science · #math.AT #cs.CG
paper · pdf · doi:10.1088/0266-5611/27/12/124003
16 pages, 3 figures, submitted to the Inverse Problems special issue on Topological Data Analysis
arxiv created 2011/07/28 · arxiv updated 2015/05/28
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.