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Title: Dualities in Persistent (Co)Homology

Abstract

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.

Authors:
; ;
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
Computational Research Division
OSTI Identifier:
1052182
Report Number(s):
LBNL-5237E
Journal ID: ISSN 0266-5611
DOE Contract Number:  
DE-AC02-05CH11231
Resource Type:
Journal Article
Journal Name:
Inverse Problems
Additional Journal Information:
Journal Volume: 27; Journal Issue: 12; Journal ID: ISSN 0266-5611
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 01 COAL, LIGNITE, AND PEAT

Citation Formats

de Silva, Vin, Morozov, Dmitriy, and Vejdemo-Johansson, Mikael. Dualities in Persistent (Co)Homology. United States: N. p., 2011. Web. doi:10.1088/0266-5611/27/12/124003.
de Silva, Vin, Morozov, Dmitriy, & Vejdemo-Johansson, Mikael. Dualities in Persistent (Co)Homology. United States. doi:10.1088/0266-5611/27/12/124003.
de Silva, Vin, Morozov, Dmitriy, and Vejdemo-Johansson, Mikael. Fri . "Dualities in Persistent (Co)Homology". United States. doi:10.1088/0266-5611/27/12/124003. https://www.osti.gov/servlets/purl/1052182.
@article{osti_1052182,
title = {Dualities in Persistent (Co)Homology},
author = {de Silva, Vin and Morozov, Dmitriy and Vejdemo-Johansson, Mikael},
abstractNote = {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.},
doi = {10.1088/0266-5611/27/12/124003},
journal = {Inverse Problems},
issn = {0266-5611},
number = 12,
volume = 27,
place = {United States},
year = {2011},
month = {9}
}