Homology Configurations

Yann-Situ Gazull (LIS)

In this talk we will present the concept of homology configuration. Homology configurations aim to capture the possible representations of the holes of an object. Precisely, they classify the explicit homology bases of an object, i.e. the homology bases that can be computed by standard approaches (persistent homology, Smith normal form, HDVF...). First, we will give the intuition and the definition of homology configurations. Then, we will present some results, particularly, homology configurations provide a low-dimension topological invariant. We will conclude with some works in progress.