2019/11/25 by José Luis Cisneros‐Molina, David Mond, Cisneros-Molina, José Luis +1 · 1 citation
Computer Science · Mathematics · #32S05 #55T99 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Digital Image Processing Techniques #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1911.11095
openalex publication_date 2019/11/25 · openalex created_date 2022/11/14 · openalex updated_date 2026/07/28
The Image-Computing Spectral Sequence computes the homology of the image of a finite map from the alternating homology of the multiple point spaces of the map. A related spectral sequence was obtained by Gabrielov, Vorobjob and Zell which computes the homology of the image of a closed map from the homology of k-fold fibred products of the map. We give new proofs of these results, in case the map can be triangulated. Thanks to work of Hardt, this holds for a very wide range of maps, and in particular for most of the finite maps of interest in singularity theory. The proof seems conceptually simpler and more canonical than earlier proofs.