Uniqueness of models in persistent homology: the case of curves

@article{Frosini2010UniquenessOM,
  title={Uniqueness of models in persistent homology: the case of curves},
  author={Patrizio Frosini and Claudia Landi},
  journal={ArXiv},
  year={2010},
  volume={abs/1012.5783}
}
We consider generic curves in , i.e. generic C1 functions . We analyze these curves through the persistent homology groups of a filtration induced on S1 by f. In particular, we consider the question whether these persistent homology groups uniquely characterize f, at least up to re-parameterizations of S1. We give a partially positive answer to this question. More precisely, we prove that f = g o h, where h: S1 ? S1 is a C1-diffeomorphism, if and only if the persistent homology groups of s o f… 

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