Noncommutativity vs gauge symmetry

Abstract

In many aspects the most complicated noncommutative spaces correspond to foliated manifolds with nonvanishing Godbillon-Vey class. We argue that gauge invariance probably prevents a foliated manifold from creating resilient leaves and thus resulting in having nonvanishing GV-class. So these spaces which are of the highest noncommutativity are not likely to appear in gauge theories.

16 pages, tex, version accepted for publication