Let N be a closed orientable n-manifold, n ≥ 3, and K a compact non-empty subset. We prove that the existence of a transversally orientable codimension one foliation on N∖K with leaves homeomorphic to , in the relative topology, implies that K must be connected. If in addition one imposes some restrictions on the homology of K, then N must be a homotopy sphere. Next we consider C² actions of a Lie group diffeomorphic to on N and obtain our main result: if K, the set of singular points of the action, is a finite non-empty subset, then K contains only one point and N is homeomorphic to Sⁿ.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap82-1-7,
author = {J. A. \'Alvarez L\'opez and J. L. Arraut and C. Biasi},
title = {Foliations by planes and Lie group actions},
journal = {Annales Polonici Mathematici},
volume = {81},
year = {2003},
pages = {61-69},
zbl = {1099.57029},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap82-1-7}
}
J. A. Álvarez López; J. L. Arraut; C. Biasi. Foliations by planes and Lie group actions. Annales Polonici Mathematici, Tome 81 (2003) pp. 61-69. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap82-1-7/