Inserted: 21 apr 2023
Last Updated: 2 oct 2023
Journal: Proceedings of the Royal Society of Edinburgh. Section A: Mathematics
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 $0$-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 $-1$.