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 Zp encompasses only the holes associated to the free part, in agreement with the rational case.
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