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The persistent homology of a sampled map: from a viewpoint of quiver representations
2021
Journal of Applied and Computational Topology
AbstractThis paper is intended to introduce a filtration analysis of sampled maps based on persistent homology, providing a new method for reconstructing the underlying maps. The key idea is to extend the definition of homology induced maps of correspondences using the framework of quiver representations. Our definition of homology induced maps is given by most persistent direct summands of representations. The direct summands uniquely determine a persistent homology. We provide stability
doi:10.1007/s41468-021-00065-3
fatcat:szyc3q2ofvawpgota7djmoifru