Multiple points of a simplicial map and image-computing spectral sequences
Journal of Singularities, Tome 24 (2022), pp. 190-212
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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, obtained by Gabrielov, Vorobjov and Zell, 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 revealing than earlier proofs.
@article{10_5427_jsing_2022_24h,
author = {Jos\'e Luis Cisneros-Molina and David Mond},
title = {Multiple points of a simplicial map and image-computing spectral sequences},
journal = {Journal of Singularities},
pages = {190--212},
publisher = {mathdoc},
volume = {24},
year = {2022},
doi = {10.5427/jsing.2022.24h},
url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2022.24h/}
}
TY - JOUR AU - José Luis Cisneros-Molina AU - David Mond TI - Multiple points of a simplicial map and image-computing spectral sequences JO - Journal of Singularities PY - 2022 SP - 190 EP - 212 VL - 24 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.5427/jsing.2022.24h/ DO - 10.5427/jsing.2022.24h ID - 10_5427_jsing_2022_24h ER -
%0 Journal Article %A José Luis Cisneros-Molina %A David Mond %T Multiple points of a simplicial map and image-computing spectral sequences %J Journal of Singularities %D 2022 %P 190-212 %V 24 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.5427/jsing.2022.24h/ %R 10.5427/jsing.2022.24h %F 10_5427_jsing_2022_24h
José Luis Cisneros-Molina; David Mond. Multiple points of a simplicial map and image-computing spectral sequences. Journal of Singularities, Tome 24 (2022), pp. 190-212. doi: 10.5427/jsing.2022.24h
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