Geometric Obstructions in Finsler Spaces and Torsion-Free Persistent Homology

Abstract: We relate the novel concept of Topological Data Analysis in Finsler space with representability property, which is a natural obstruction to prevent spurious features in high dimensions. We use decomposition of integer matrix in order to find suitable prime integer $p$ such that persistent homology module over $\mathbb{Z}_p$ encompasses only the holes associated to the free part, in agreement with the rational case.