Persistence of common topological structures by commutative triple ladder quiver

Emerson G. Escolar, Yasuaki Hiraoka

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This is a summary paper of Escolar and Hiraoka (Persistence modules on commutative ladders of finite type. Discrete Comput Geom 55, 100-157 (2016)) which presents an extension of persistence modules as representations on quivers with nontrivial relations. In particular, the mathematical and algorithmic results in that paper enable us to detect robust and common topological structures of two geometric objects. In this paper, we only deal with a special type of persistencemodules defined on the so-called commutative triple ladder for the sake of simplicity.We aim to explain the essence of Auslander-Reiten theory in connection with persistence modules.

Original languageEnglish
Title of host publicationMathematical Challenges in a New Phase of Materials Science
EditorsYasumasa Nishiura, Motoko Kotani
PublisherSpringer New York LLC
Pages69-82
Number of pages14
ISBN (Print)9784431561026
DOIs
Publication statusPublished - 2016
EventInternational Conference on Mathematical Challenges in a New Phase of Materials Science, 2014 - Kyoto, Japan
Duration: 2014 Aug 42014 Aug 8

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume166
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

OtherInternational Conference on Mathematical Challenges in a New Phase of Materials Science, 2014
CountryJapan
CityKyoto
Period14/8/414/8/8

Keywords

  • Commutative triple ladder
  • Persistence modules
  • Representation theory
  • Topological data analysis

ASJC Scopus subject areas

  • Mathematics(all)

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