Dualities in persistent (co)homology

We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establishalgebraic relationships between their persistence modules, and show that they contain equivalent information. We explain how one can use the existingalgorithm f...

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Bibliographic Details
Published inInverse problems Vol. 27; no. 12; p. 124003
Main Authors de Silva, Vin, Morozov, Dmitriy, Vejdemo-Johansson, Mikael
Format Journal Article
LanguageEnglish
Published United States IOP Publishing 01.12.2011
Subjects
01 COAL, LIGNITE, AND PEAT
MATHEMATICS AND COMPUTING
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Summary:We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establishalgebraic relationships between their persistence modules, and show that they contain equivalent information. We explain how one can use the existingalgorithm for persistent homology to process any of the four modules, and relate it to a recently introduced persistent cohomology algorithm. Wepresent experimental evidence for the practical efficiency of the latter algorithm.
Bibliography:LBNL-5237E
Computational Research Division
DE-AC02-05CH11231
ISSN:0266-5611
1361-6420
1361-6420
DOI:10.1088/0266-5611/27/12/124003