Multiple points of a simplicial map and image-computing spectral sequences
José Luis Cisneros‐Molina, David Mond · Journal of Singularities · 2022
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 in [GVZ04] 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 in [Har77], 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.