Optimising the topological information of the A8-persistence groups
Persistent homology typically studies the evolution of homology groups Hp(X) (with coefficients in a field) along a filtration of topological spaces. A8-persistence extends this theory by analysing the evolution of subspaces such as V:=Ker¿n|Hp(X)¿Hp(X), where {¿m}m=1 denotes a structure of A8-coalg...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/177949 |
| Acceso en línea: | https://hdl.handle.net/2117/177949 https://dx.doi.org/10.1007/s00454-019-00094-x |
| Access Level: | acceso abierto |
| Palabra clave: | Persistent homology Zigzag persistence A8-persistence Topological data analysis A8-(co)algebras Massey products Knot theory Rational homotopy theory Spectral sequences Classificació AMS::16 Associative rings and algebras::16E Homological methods Classificació AMS::18 Category theory homological algebra::18G Homological algebra Classificació AMS::55 Algebraic topology::55S Operations and obstructions Classificació AMS::57 Manifolds and cell complexes::57M Low-dimensional topology Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra |
| Sumario: | Persistent homology typically studies the evolution of homology groups Hp(X) (with coefficients in a field) along a filtration of topological spaces. A8-persistence extends this theory by analysing the evolution of subspaces such as V:=Ker¿n|Hp(X)¿Hp(X), where {¿m}m=1 denotes a structure of A8-coalgebra on H*(X). In this paper we illustrate how A8-persistence can be useful beyond persistent homology by discussing the topological meaning of V, which is the most basic form of A8-persistence group. In addition, we explore how to choose A8-coalgebras along a filtration to make the A8-persistence groups carry more faithful information. |
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