Simple topological measures and a lifting problem

Abstract

This paper is dedicated to my colleague Johan Aarnes who has introduced me and many others to tread on this beautiful virgin ground where exotic topological measures liveAbstract. We state a certain lifting conjecture and prove it in the case of a torus. From this result we are able to construct a connected dense subset of the space of intrinsic simple topological measures on the torus, consisting of push forwards of compactly supported generalized point-measures on the universal covering space. Combining this result with an observation of Johansen and Rustad, we conclude that the space of simple topological measures on a torus is connected. Contents