B3 Moduli spaces of metrics of positive curvature

We will develop a family version of coarse index theory which encompasses all existing index invariants for the understanding of spaces of positive scalar curvature (psc) metrics—the higher family index and index difference—as well as new ones such as family rho-invariants. This will enable the detection of new non-trivial elements in homotopy groups of certain moduli spaces of psc metrics. We will also further study the concordance space of psc metrics together with appropriate index maps.