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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm200-3-1,
author = {Finn F. Knudsen},
title = {Simple topological measures and a lifting problem},
journal = {Fundamenta Mathematicae},
volume = {201},
year = {2008},
pages = {201-241},
zbl = {1155.28002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm200-3-1}
}
Finn F. Knudsen. Simple topological measures and a lifting problem. Fundamenta Mathematicae, Tome 201 (2008) pp. 201-241. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm200-3-1/