From the Mayer-Vietoris spectral sequence to überhomology
arXiv:2304.10134 · doi:10.1017/prm.2023.104
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 überhomology. 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 .
18 pages, comments are welcome! V2 published version