Exterior Critical Series of Persistence Modules

The persistence barcode is a well-established complete discrete invariant for finitely generated persistence modules [5] [1]. Its definition, however, does not extend to multi-dimensional persistence modules. In this paper, we introduce a new discrete invariant: the exterior critical series. This invariant is complete in the one-dimensional case and can be defined for multi-dimensional persistence modules, like the rank invariant [2]. However, the exterior critical series can detect some features that are not captured by the rank invariant.