Asymptotic geometry and growth of conjugacy classes of nonpositively curved manifolds
نویسنده
چکیده
Let X be a Hadamard manifold and Γ ⊂ Isom(X) a discrete group of isometries which contains an axial isometry without invariant flat half plane. We study the behavior of conformal densities on the limit set of Γ in order to derive a new asymptotic estimate for the growth rate of closed geodesics in not necessarily compact or finite volume manifolds.
منابع مشابه
Conjugacy rigidity for nonpositively curved graph manifolds
We show that the metric of nonpositively curved graph manifolds is determined by its geodesic flow. More precisely we show that if the geodesic flows of two nonpositively curved graph manifolds are C0 conjugate then the spaces
متن کاملGeodesic Flows in Manifolds of Nonpositive Curvature
I. Introduction-a quick historical survey of geodesic flows on negatively curved spaces. II. Preliminaries on Riemannian manifolds A. Riemannian metric and Riemannian volume element B. Levi Civita connection and covariant differentiation along curves C. Parallel translation of vectors along curves D. Curvature E. Geodesics and geodesic flow F. Riemannian exponential map and Jacobi vector fields...
متن کاملVirtual Cubulation of Nonpositively Curved Graph Manifolds
In this paper, we show that an aspherical compact graph manifold is nonpositively curved if and only if its fundamental group virtually embeds into a right-angled Artin group. As a consequence, nonpositively curved graph manifolds have linear fundamental groups.
متن کاملOn actions of discrete groups on nonpositively curved spaces
This note contains several observations concerning discrete groups of non-parabolic isometries of spaces of nonpositive curvature. We prove that (almost all) surface mapping class groups do not admit such actions; in particular, they do not act cocompactly. A new obstruction to the existence of a nonpositively curved metric on closed manifolds is presented. We give examples of 4-manifolds bered...
متن کاملEspaces de représentations complètement réductibles
We study some geometric properties of actions on nonpositively curved spaces related to complete reducibility and semisimplicity, focusing on representations of a finitely generated group Γ in the group G of rational points of a reductive group over a local field, acting on the associated space (symmetric space or affine building). We prove that the space of completely reducible classes is the ...
متن کامل