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 -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 .
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