Groups in the category of f-manifolds
Groups of -diffeomorphisms related to a foliation
The notion of a -diffeomorphism related to a foliation is introduced. A perfectness theorem for the group of -diffeomorphisms is proved. A remark on -diffeomorphisms is given.
Groups of piecewise linear homeomorphisms of the real line.
Groups of real analytic diffeomorphisms of the circle with a finite image under the rotation number function
We consider groups of orientation-preserving real analytic diffeomorphisms of the circle which have a finite image under the rotation number function. We show that if such a group is nondiscrete with respect to the -topology then it has a finite orbit. As a corollary, we show that if such a group has no finite orbit then each of its subgroups contains either a cyclic subgroup of finite index or a nonabelian free subgroup.
Groups of transformations of a G-structure whic H leave invariant a substructure.
Groups with Domains of Discontinuity.
Groups with no infinite perfect subgroups and aspherical 2-complexes.
Group-theoretic conditions under which closed aspherical manifolds are covered by Euclidean space
Hass, Rubinstein, and Scott showed that every closed aspherical (irreducible) 3-manifold whose fundamental group contains the fundamental group of a closed aspherical surface, is covered by Euclidean space. This theorem does not generalize to higher dimensions. However, we provide geometric tools with which variations of this theorem can be proved in all dimensions.
Growth functions of surface groups.
Growth functions on Fuchsian groups and the Euler characteristic.
Growth of a primitive of a differential form
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...
Growth of Jacobi Fields and Divergence of Geodesics.
Growth of leaves.