Persistence Module and Leray’s Theorem for Persistence Module

The concept of persistence emerged independently in the work of Frosini, Ferri, and collaborators in Bologna, Italy, in the doctoral work of Robins at Boulder, Colorado, and within the biogeometry project of Edelsbrunner at Duke, North Carolina.

Persistent homology/cohomology is an algebraic method for measuring topological features of shapes and of functions. In the last 20 years the research and application of persistent homology/cohomology has been intense.

In this talk I will to show that the persistent cohomology of a filtered finite dimensional simplicial complex is a graded module over a polynomial ring, like Zomorodian and Gunnar had done to persistent homology and I will show an extension of Leray's theorem for persistence module.