Retrieving biparameter persistence modules from monoparameter ones: a characterization of hook-decomposable persistence modules

Motivated by the need to relate the biparameter persistence module induced by a pair of scalar functions with the monoparameter persistence modules induced by each function separately, we introduce a construction that defines a kind of product between two monoparameter persistence modules. While originally conceived to serve this comparative purpose, our construction unexpectedly reveals a deeper structural property: it also characterizes a class of biparameter modules known as hook-decomposable modules.

💡 Research Summary

The paper addresses the problem of relating a biparameter persistence module induced by a pair of scalar functions f and g to the monoparameter persistence modules induced by each function individually. Working under the finite‑type assumption, the authors identify the monoparameter modules M_f and M_g with finitely generated graded modules over the polynomial rings F