A T ] 2 8 M ay 2 01 8 The reflection distance between zigzag persistence modules

By invoking the reflection functors introduced by Bernstein, Gelfand, and Ponomarev in 1973, in this paper we define a metric on the space of all zigzag modules of a given length, which we call the reflection distance. We show that the reflection distance between two given zigzag modules of the same length is an upper bound for the l -bottleneck distance between their respective persistence diagrams.