@article{carlssonTheoryMultidimensionalPersistence2009,
  langid = {english},
  title = {The {{Theory}} of {{Multidimensional Persistence}}},
  volume = {42},
  issn = {0179-5376, 1432-0444},
  url = {https://link.springer.com/article/10.1007/s00454-009-9176-0},
  doi = {10.1007/s00454-009-9176-0},
  abstract = {Persistent homology captures the topology of a filtration—a one-parameter family of increasing spaces—in terms of a complete discrete invariant. This invariant is a multiset of intervals that denote the lifetimes of the topological entities within the filtration. In many applications of topology, we need to study a multifiltration: a family of spaces parameterized along multiple geometric dimensions. In this paper, we show that no similar complete discrete invariant exists for multidimensional persistence. Instead, we propose the rank invariant, a discrete invariant for the robust estimation of Betti numbers in a multifiltration, and prove its completeness in one dimension.},
  number = {1},
  journaltitle = {Discrete \& Computational Geometry},
  shortjournal = {Discrete Comput Geom},
  urldate = {2018-04-30},
  date = {2009-07-01},
  pages = {71-93},
  author = {Carlsson, Gunnar and Zomorodian, Afra},
  file = {/home/dimitri/Nextcloud/Zotero/storage/4EEYB2MK/10.1.1.86.1620.pdf;/home/dimitri/Nextcloud/Zotero/storage/RBN5LKT6/Carlsson and Zomorodian - 2009 - The Theory of Multidimensional Persistence.pdf;/home/dimitri/Nextcloud/Zotero/storage/PT7Q4KVU/10.html}
}

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