Decomposition of exact pfd persistence bimodules
Résumé
We identify a certain class of persistence modules indexed over R2 that are decomposable into direct sums of indecomposable summands called blocks. The conditions on the modules are that they are both pointwise finite-dimensional (pfd) and exact. Our proof follows the same scheme as the one for pfd persistence modules indexed over R, yet it departs from it at key stages due to the product order not being a total order on R2, which leaves some important gaps open. These gaps are filled in using more direct arguments. Our work is motivated primarily by the study of interlevel-sets persistence, although the proposed results reach beyond that setting.