English

Multiple points of a simplicial map and image-computing spectral sequences

Algebraic Topology 2019-11-26 v1 Algebraic Geometry

Abstract

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 kk-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.

Keywords

Cite

@article{arxiv.1911.11095,
  title  = {Multiple points of a simplicial map and image-computing spectral sequences},
  author = {José Luis Cisneros-Molina and David Mond},
  journal= {arXiv preprint arXiv:1911.11095},
  year   = {2019}
}

Comments

20 pages

R2 v1 2026-06-23T12:26:45.107Z