The Multi-Cover Persistence of Euclidean Balls.

Given a locally finite and a radius , the - of and consists of all points in that have or more points of within distance . We consider two filtrations-one in obtained by fixing and increasing , and the other in obtained by fixing and decreasing -and we compute the persistence diagrams of both. While standard methods suffice for the filtration in scale, we need novel geometric and topological concepts for the filtration in depth. In particular, we introduce a rhomboid tiling in  whose horizontal integer slices are the order- Delaunay mosaics of , and construct a zigzag module of Delaunay mosaics that is isomorphic to the persistence module of the multi-covers.