License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2018.15
URN: urn:nbn:de:0030-drops-87287
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8728/
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Buchet, Mickaël ; Escolar, Emerson G.

Realizations of Indecomposable Persistence Modules of Arbitrarily Large Dimension

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Abstract

While persistent homology has taken strides towards becoming a widespread tool for data analysis, multidimensional persistence has proven more difficult to apply. One reason is the serious drawback of no longer having a concise and complete descriptor analogous to the persistence diagrams of the former. We propose a simple algebraic construction to illustrate the existence of infinite families of indecomposable persistence modules over regular grids of sufficient size. On top of providing a constructive proof of representation infinite type, we also provide realizations by topological spaces and Vietoris-Rips filtrations, showing that they can actually appear in real data and are not the product of degeneracies.

BibTeX - Entry

@InProceedings{buchet_et_al:LIPIcs:2018:8728,
  author =	{Micka{\"e}l Buchet and Emerson G. Escolar},
  title =	{{Realizations of Indecomposable Persistence Modules of Arbitrarily Large Dimension}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{15:1--15:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8728},
  URN =		{urn:nbn:de:0030-drops-87287},
  doi =		{10.4230/LIPIcs.SoCG.2018.15},
  annote =	{Keywords: persistent homology, multi-persistence, representation theory, quivers, commutative ladders, Vietoris-Rips filtration}
}

Keywords: persistent homology, multi-persistence, representation theory, quivers, commutative ladders, Vietoris-Rips filtration
Collection: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 08.06.2018

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