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arXiv · 2006.13793

Decomposition of Pointwise Finite-Dimensional S^1 Persistence Modules

Eric J. Hanson·Job D. Rock
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Abstract

We prove that pointwise finite-dimensional S^1 persistence modules over an arbitrary field decompose uniquely, up to isomorphism, into the direct sum of a bar code and finitely-many Jordan cells. These persistence modules have also been called angle-valued or circular persistence modules. We allow either a cyclic order or partial order on S^1 and do not have additional finiteness requirements on the modules. We also show that a pointwise finite-dimensional S^1 persistence module is indecomposable if and only if it is a bar or Jordan cell (a string or a band module, respectively, in representation theory). Along the way we classify the isomorphism classes of such indecomposable modules.

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BibTeXRIS

Eric J. Hanson, Job D. Rock. 2020-06-24. Decomposition of Pointwise Finite-Dimensional S^1 Persistence Modules. https://doi.org/10.1142/s0219498824500543

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