Grafting Seiberg-Witten monopoles.
Let M be a manifold with a regular foliation F. We recall the construction of the fundamental groupoid and the homotopy groupoid associated to F. We describe some interesting particular cases and give some glueing techniques. We characterize the cases where these groupoids are Hausdorff spaces.We study in particular both groupoids associated to foliations with Reeb components.
For an exact differential form on a Riemannian manifold to have a primitive bounded by a given function , by Stokes it has to satisfy some weighted isoperimetric inequality. We show the converse up to some constants if has bounded geometry. For a volume form, it suffices to have the inequality ( for every compact domain ). This implies in particular the “well-known” result that if is the universal covering of a compact Riemannian manifold with non-amenable fundamental group, then the volume...