Decomposition of Pointwise Finite-Dimensional S^1 Persistence Modules

Eric J. Hanson, Job D. Rock

Published 2020-06-24Version 1

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 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 the language of representation theory).