Uberhomology, combinatorics and the Mayer-Vietoris spectral sequence

In this talk we will introduce uberhomology, a combinatorially defined homology theory for simplicial complexes. After proving some of its properties, we’ll show how this invariant is related to dominating sets and to the Mayer-Vietoris spectral sequence. We will conclude with some open questions and problems. All results are joint work with L. Caputi and D. Celoria.