TY - GEN

T1 - Persistence of common topological structures by commutative triple ladder quiver

AU - Escolar, Emerson G.

AU - Hiraoka, Yasuaki

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Commutative triple ladder

KW - Persistence modules

KW - Representation theory

KW - Topological data analysis

UR - http://www.scopus.com/inward/record.url?scp=84978886784&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84978886784&partnerID=8YFLogxK

U2 - 10.1007/978-4-431-56104-0_4

DO - 10.1007/978-4-431-56104-0_4

M3 - Conference contribution

AN - SCOPUS:84978886784

SN - 9784431561026

T3 - Springer Proceedings in Mathematics and Statistics

SP - 69

EP - 82

BT - Mathematical Challenges in a New Phase of Materials Science

A2 - Nishiura, Yasumasa

A2 - Kotani, Motoko

PB - Springer New York LLC

T2 - International Conference on Mathematical Challenges in a New Phase of Materials Science, 2014

Y2 - 4 August 2014 through 8 August 2014

ER -