AbstractWe will introduce the general twistor space picture for moduli spaces of connections deforming to moduli spaces of Higgs bundles, initiated by Hitchin for his hyperkähler structure. The Deligne-Hitchin twistor space construction has a property analogous to weight 1 Hodge structures.This may be extended to twistor structures of other weights. In the case of moduli theory of connections o...
Abstract:I will describe a complete set of numerical invariants for deciding whether a real vector bundle is stably trivial. These invariants are integers and rational angles which will be a priori given in contrast to the usual theory of secondary characteristic classes. The definition of these invariants features a duality between the reals and quaternions, moreover a quaternionic version of...