quadratic cohomology Archives

Quadratic Cohomology

By oliverknill June 30, 2024 June 30, 2024

I looked at a quadratic cohomology example. For theoretical backgroun, see the ArXiv paper “Fusion inequality for quadratic cohomology”. It is the case when U is a union of two disjoint smallest open sets in a 2-sphere for which I take the Icosahedron, one of the Platonic solids and a …

simplicial complex, Spectral Theory

Fusion Inequality for Quadratic Cohomology

By oliverknill June 23, 2024 June 30, 2024

While linear cohomology deals with functions on simplices, quadratic cohomology deals with functions on pairs of simplices that intersect. Linear cohomology is to Euler characteristic what quadratic cohomology is to Wu characteristic $w(G) = \sum_{x,y, x \cap y \in G} w(x) w(y)$. If the simplicial complex is split into a …