Double complexes for configuration spaces and hypergraphs on manifolds

Abstract: In this talk, we consider hypergraphs whose vertices are distinct points moving smoothly on a Riemannian manifold. We take these hypergraphs as graded submanifolds of configuration spaces. We construct double complexes of differential forms on configuration spaces. Then we construct double complexes of differential forms on hypergraphs, which are sub-double complexes of the double complex for the ambient configuration space. Among these double complexes for hypergraphs, the infimum double complex and the supremum double complex are quasi-isomorphic concerning the boundary maps induced from vertex deletion of the hyperedges. In particular, all the double complexes are identical if the hypergraph is a Delta-submanifold of the ambient configuration space. We will discuss the restriction condition and the extension condition in order to make the arguments strict.

mathematical physicsalgebraic geometryalgebraic topologygeometric topologyquantum algebra

Audience: researchers in the topic

Moscow-Beijing topology seminar

Series comments: https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1h.. Meeting ID: 818 6674 5751 Passcode: 141592