Dualities in persistent (co)homology

Abstract

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