Let A be a symmetrizable affine or hyperbolic generalized Cartan matrix. Let G be a locally compact Kac-Moody group associated to A over a finite field Fq. We suppose that G has type ∞, that is, the Weyl group W of G is a free product of Z/2Z’s. This includes all locally compact Kac-Moody groups of rank 2 and three possible locally compact rank 3 Kac-Moody groups of noncompact hyperbolic type. ...

We show the quasiconformal stability for torsion-free convex cocompact Kleinian groups acting on higher dimensional hyperbolic spaces. As an application, we prove an embedding theorem of a space of flat conformal structures on a certain class of compact manifolds.

We show that not every Salem number appears as the growth rate of a cocompact hyperbolic Coxeter group. also give new proof fact rates planar groups are spectral radii transformations, and this need be case for tetrahedral groups.

Reid asked whether all convex-cocompact subgroups of mapping class groups are separable. Using a construction Manning–Mj–Sageev, we give examples separable that free arbitrary finite rank, while prior seem to be virtually cyclic.

We study t-structures generated by sets of objects which satisfy a condition weaker than the compactness. also weight structures cogenerated satisfying dual condition. Under some appropriate hypothesis, it turns out that structure is right adjacent to t-structure.

Abstract We prove that the hitting measure is singular with respect to Lebesgue for random walks driven by finitely supported measures on cocompact, hyperelliptic Fuchsian groups. Moreover, Hausdorff dimension of strictly less than one. Equivalently, inequality between entropy and drift strict. A similar statement proven Coxeter

In this paper, we show that given a set of lengths closed geodesics, there are only finitely many convex cocompact hyperbolic 3-manifolds with specified length spectrum multiplicity, homotopy equivalent to 3-manifold without handlebody factor, up orientation preserving isometries.

The energy of harmonic sections of flat bundles of nonpositively curved (NPC) length spaces over a Riemann surface S is a function Eρ on Teichmüller space TS which is a qualitative invariant of the holonomy representation ρ of π1(S). Adapting ideas of Sacks-Uhlenbeck, Schoen-Yau and Tromba, we show that the energy function Eρ is proper for any convex cocompact representation of the fundamental ...