The Persistent Homotopy Type Distance

@article{Frosini2019ThePH,
  title={The Persistent Homotopy Type Distance},
  author={Patrizio Frosini and Claudia Landi and Facundo M{\'e}moli},
  journal={ArXiv},
  year={2019},
  volume={abs/1702.07893}
}
We introduce the persistent homotopy type distance dHT to compare real valued functions defined on possibly different homotopy equivalent topological spaces. The underlying idea in the definition of dHT is to measure the minimal shift that is necessary to apply to one of the two functions in order that the sublevel sets of the two functions become homotopically equivalent. This distance is interesting in connection with persistent homology. Indeed, our main result states that dHT still provides… 

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