English

From the Mayer-Vietoris spectral sequence to \"uberhomology

Geometric Topology 2023-10-05 v2 Algebraic Topology Combinatorics

Abstract

We prove that the second page of the Mayer-Vietoris spectral sequence, with respect to anti-star covers, can be identified with another homological invariant of simplicial complexes: the 00-degree \"uberhomology. Consequently, we obtain a combinatorial interpretation of the second page of the Mayer-Vietoris sequence in this context. This interpretation is then used to extend the computations of bold homology, which categorifies the connected domination polynomial at 1-1.

Keywords

Cite

@article{arxiv.2304.10134,
  title  = {From the Mayer-Vietoris spectral sequence to \"uberhomology},
  author = {Luigi Caputi and Daniele Celoria and Carlo Collari},
  journal= {arXiv preprint arXiv:2304.10134},
  year   = {2023}
}

Comments

18 pages, comments are welcome! V2 published version