Optimising the Topological Information of the A∞-Persistence Groups
Persistent homology typically studies the evolution of homology groups Hp(X) (with coefficients in a field) along a filtration of topological spaces. A∞-persistence extends this theory by analysing the evolution of subspaces such as V:=KerΔn|Hp(X)⊆Hp(X), where {Δm}m≥1 denotes a structure of A∞-coalg...
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/202286 |
| Acceso en línea: | http://hdl.handle.net/10261/202286 |
| Access Level: | acceso abierto |
| Palabra clave: | Persistent homology Zigzag persistence A∞-persistence Topological data analysis A∞-(co)algebras Massey products Knot theory Rational homotopy theory Spectral sequences |
| Sumario: | Persistent homology typically studies the evolution of homology groups Hp(X) (with coefficients in a field) along a filtration of topological spaces. A∞-persistence extends this theory by analysing the evolution of subspaces such as V:=KerΔn|Hp(X)⊆Hp(X), where {Δm}m≥1 denotes a structure of A∞-coalgebra on H∗(X). In this paper we illustrate how A∞-persistence can be useful beyond persistent homology by discussing the topological meaning of V, which is the most basic form of A∞-persistence group. In addition, we explore how to choose A∞-coalgebras along a filtration to make the A∞-persistence groups carry more faithful information. |
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