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arXiv · 1302.2015

Persistence modules: Algebra and algorithms

Primoz Skraba·Mikael Vejdemo-Johansson
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Abstract

Persistent homology was shown by Carlsson and Zomorodian to be homology of graded chain complexes with coefficients in the graded ring $\kk[t]$. As such, the behavior of persistence modules -- graded modules over $\kk[t]$ is an important part in the analysis and computation of persistent homology. In this paper we present a number of facts about persistence modules; ranging from the well-known but under-utilized to the reconstruction of techniques to work in a purely algebraic approach to persistent homology. In particular, the results we present give concrete algorithms to compute the persistent homology of a simplicial complex with torsion in the chain complex.

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Primoz Skraba, Mikael Vejdemo-Johansson. 2013-02-08. Persistence modules: Algebra and algorithms. https://arxiv.org/abs/1302.2015

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