Title: Erosion distance for generalized persistence modules,
Abstract: The persistence diagram of Cohen-Steiner, Edelsbrunner, and Harer was
recently generalized by Patel to the case of constructible persistence modules
with values in a symmetric monoidal category with images. Patel also introduced
a distance for persistence diagrams, the erosion distance. Motivated by this
work, we extend the erosion distance to a distance of rank invariants of
generalized persistence modules by using the generalization of the interleaving
distance of Bubenik, de Silva, and Scott as a guideline. This extension of the
erosion distance also gives, as a special case, a distance for multidimensional
persistent homology groups with torsion introduced by Frosini. We show that the
erosion distance is stable with respect to the interleaving distance, and that
it gives a lower bound for the natural pseudo-distance in the case of sublevel
set persistent homology of continuous functions.