dc.contributor.author
Belchi Guillamon, Francisco
dc.identifier
Belchi, F. Optimising the topological information of the A8-persistence groups. "Discrete and computational geometry", 2019, vol. 62, núm. 1, p. 29-54.
dc.identifier
https://arxiv.org/abs/1706.06019
dc.identifier
https://hdl.handle.net/2117/177949
dc.identifier
10.1007/s00454-019-00094-x
dc.description.abstract
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.
dc.description.abstract
Peer Reviewed
dc.description.abstract
Postprint (author's final draft)
dc.format
application/pdf
dc.relation
https://link.springer.com/article/10.1007%2Fs00454-019-00094-x
dc.subject
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
dc.subject
Persistent homology
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Zigzag persistence
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A8-persistence
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Topological data analysis
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A8-(co)algebras
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Massey products
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Rational homotopy theory
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Spectral sequences
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Classificació AMS::16 Associative rings and algebras::16E Homological methods
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Classificació AMS::18 Category theory; homological algebra::18G Homological algebra
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Classificació AMS::55 Algebraic topology::55S Operations and obstructions
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Classificació AMS::57 Manifolds and cell complexes::57M Low-dimensional topology
dc.title
Optimising the topological information of the A8-persistence groups
