2026-04-18T07:54:05Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/1779492026-01-27T03:58:21Zcom_2072_1033col_2072_452950

Optimising the topological information of the A8-persistence groups Belchi Guillamon, Francisco Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra 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 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. Peer Reviewed Postprint (author's final draft) 2019 Article Belchi, F. Optimising the topological information of the A8-persistence groups. "Discrete and computational geometry", 2019, vol. 62, núm. 1, p. 29-54. 0179-5376 https://arxiv.org/abs/1706.06019 https://hdl.handle.net/2117/177949 10.1007/s00454-019-00094-x eng https://link.springer.com/article/10.1007%2Fs00454-019-00094-x Open Access 26 p. application/pdf