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The persistent homology with coefficients in a field F coincides with thesame for cohomology because of duality. We propose an implementation of arecently introduced algorithm for persistent cohomology that attachesannotation vectors with the simplices. We separate the representation of thesimplicial complex from the representation of the cohomology groups, andintroduce a new data structure for maintaining the annotation matrix, which ismore compact and reduces substancially the amount of matrix operations. Inaddition, we propose heuristics to simplify further the representation of thecohomology groups and improve both time and space complexities. The paperprovides a theoretical analysis, as well as a detailed experimental study ofour implementation and comparison with state-of-the-art software for persistenthomology and cohomology.

The Compressed Annotation Matrix: an Efficient Data Structure for Computing Persistent Cohomology