Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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L. Caputi - D. Celoria - C. Collari

From the Mayer-Vietoris spectral sequence to ├╝berhomology

created by collari on 21 Apr 2023
modified on 02 Oct 2023

[BibTeX]

Published Paper

Inserted: 21 apr 2023
Last Updated: 2 oct 2023

Journal: Proceedings of the Royal Society of Edinburgh. Section A: Mathematics
Year: 2023
Doi: 10.1017/prm.2023.104

ArXiv: 2304.10134 PDF

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 $0$-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 $-1$.

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