Bridging between überhomology and double homology
arXiv:2406.18778
Abstract
We establish an isomorphism between the 0-degree überhomology and the double homology of finite simplicial complexes, using a Mayer-Vietoris spectral sequence argument. We clarify the correspondence between these theories by providing examples and some consequences; in particular, we show that überhomology groups detect the standard simplex, and that the double homology's diagonal is related to the connected domination polynomial.
12 pages, comments are welcome! Updated version incorporating referee feedback