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.
Halbeinfache Automorphismengruppen von vierdimensionalen stabilen Ebenen sind quasi-einfach.
Halves of a real Enriques surface.
Handle attaching in symplectic homology and the Chord Conjecture
Arnold conjectured that every Legendrian knot in the standard contact structure on the 3-sphere possesses a haracteristic chord with respect to any contact form. I confirm this conjecture if the know has Thurston-Bennequin invariant . More generally, existence of chords is proved for a standard Legendrian unknot on the boundary of a subcritical Stein manifold of any dimension. There is also a multiplicity result which implies in some situations existence of infinitely many chords. The proof relies...
Handlebody splittings of compact 3-manifolds with boundary.
The purpose of this paper is to relate several generalizations of the notion of the Heegaard splitting of a closed 3-manifold to compact, orientable 3-manifolds with nonempty boundary.
Handle-decompositions of -manifolds
Hardness of embedding simplicial complexes in
Let be the following algorithmic problem: Given a finite simplicial complex of dimension at most , does there exist a (piecewise linear) embedding of into ? Known results easily imply polynomiality of (; the case is graph planarity) and of for all . We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that and are undecidable for each . Our main result is NP-hardness of and, more generally, of for all , with...
Harmonic Analysis for Vector Fields on Hyperbolic Spaces.
Harmonic and Minimal Unit Vector Fields on the Symmetric Spaces and
The exceptional compact symmetric spaces and admit cohomogeneity one isometric actions with two totally geodesic singular orbits. These singular orbits are not reflective submanifolds of the ambient spaces. We prove that the radial unit vector fields associated to these isometric actions are harmonic and minimal.
Harmonic Maps and the Topology of Stable Hypersurfaces and Manifolds with Non-negative Ricci Curvature