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From the Mayer–Vietoris spectral sequence to überhomology
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
- Published online by Cambridge University Press:
- 02 October 2023, pp. 1-24
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- Article
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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 überhomology. Consequently, we obtain a combinatorial interpretation of the second page of the Mayer–Vietoris spectral sequence in this context. This interpretation is then used to extend the computations of bold homology, which categorifies the connected domination polynomial at $-1$
.
