Discrete Vector Fields and Fundamental Algebraic Topology

2010/05/31 by Ana Romero, Romero, Ana, Francis Sergeraert +1 · 1 citation
Computer Science · Mathematics · #18G30 #18G40 #55P20 #55T10 #55T20 #55T35 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #cs.DM #math.AT #msc:18G30 #msc:18G40 #msc:55P20 #msc:55T10 #msc:55T20 #msc:55T35

paper · pdf · doi:10.48550/arxiv.1005.5685

53 pages

arxiv created 2010/05/31 · openalex publication_date 2010/05/31 · arxiv updated 2010/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Simple Homotopy Types

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