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Discrete Vector Fields and Fundamental Algebraic Topology

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arxiv 1005.5685 v1 pith:RWVTYRU7 submitted 2010-05-31 math.AT cs.DM

Ana Romero , Francis Sergeraert This is my paper · ORCID
classification math.ATcs.DM
keywords algebraicdiscreteequivalencesexistencefieldsfundamentalhomologyobtained
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We show in this text how the most important homology equivalences of fundamental Algebraic Topology can be obtained as reductions associated to discrete vector fields. Mainly the homology equivalences whose existence -- most often non-constructive -- is proved by the main spectral sequences, the Serre and Eilenberg-Moore spectral sequences. On the contrary, the constructive existence is here systematically looked for and obtained.

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  1. Cycle-Decorated Ribbon Bar Complexes: Cut Factorization and Equivariant Homology

    math.CO 2026-08 conditional novelty 7.0 of 10

    A decoration by ordinary and rooted cycles on ordered set partitions yields a cut-factorization theorem that computes the full bigraded S_n-homology of the resulting ribbon bar complexes.

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