Simple topological measures and a lifting problem
Volume 200 / 2008
Fundamenta Mathematicae 200 (2008), 201-241
MSC: Primary 28A25; Secondary 28A51.
DOI: 10.4064/fm200-3-1
Abstract
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.
