Transverse G-structures on foliated mani- folds
The Hausdorff dimension of the holonomy pseudogroup of a codimension-one foliation ℱ is shown to coincide with the Hausdorff dimension of the space of compact leaves (traced on a complete transversal) when ℱ is non-minimal, and to be equal to zero when ℱ is minimal with non-trivial leaf holonomy.
A foliation of a manifold is transversely homogeneous if it can be defined by local submersions to a homogeneous space which on overlaps differ by translations. We explore the topology and geometry of such foliations and give a structure theorem for the case when is compact. We investigate the relationship between the structure equations of and the normal bundle of the foliation and provide a differential forms characterization of a large class of homogeneous foliations. As a special case,...
Let M be a 4-manifold which admits a free circle action. We use twisted Alexander polynomials to study the existence of symplectic structures and the minimal complexity of surfaces in M. The results on the existence of symplectic structures summarize previous results of the authors in [FV08a,FV08,FV07]. The results on surfaces of minimal complexity are new.