Dualities in Persistent (Co)Homology

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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.

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de Silva, Vin; Morozov, Dmitriy & Vejdemo-Johansson, Mikael September 16, 2011.

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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.

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  • Journal Name: Inverse Problems; Journal Volume: 27; Journal Issue: 12

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  • Report No.: LBNL-5237E
  • Grant Number: DE-AC02-05CH11231
  • DOI: 10.1088/0266-5611/27/12/124003 | External Link
  • Office of Scientific & Technical Information Report Number: 1052182
  • Archival Resource Key: ark:/67531/metadc828633

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  • September 16, 2011

Added to The UNT Digital Library

  • May 19, 2016, 9:45 a.m.

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  • Nov. 7, 2016, 8:16 p.m.

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de Silva, Vin; Morozov, Dmitriy & Vejdemo-Johansson, Mikael. Dualities in Persistent (Co)Homology, article, September 16, 2011; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc828633/: accessed June 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.