Related papers: Hyperbolic manifolds with geodesic boundary which …

Let $M$ be a compact oriented 3-manifold with non-empty boundary consisting of surfaces of genii $>1$ such that the interior of $M$ is hyperbolizable. We show that for each spherical cone-metric $d$ on $\partial M$ such that all cone-angles…

Let X be an arbitrary hyperbolic geodesic metric space and let G be a countable non-elementary weakly acylindrical group of isometries of X. We show that the second bounded cohomology group of G with real coefficients or with coefficients…

We study spaces obtained from a complete finite volume complex hyperbolic n-manifold M by removing a compact totally geodesic complex (n-1)-submanifold. The main result is that the fundamental group of M-S is relatively hyperbolic, relative…

Let M be an oriented complete hyperbolic n-manifold of finite volume. Using the definition of volume of a representation previously given by the authors in [BucherBurgerIozzi2013] we show that the volume of a representation of the…

We study isometric immersions $f: M^n \rightarrow \mathbb{H}^{n+1}$ into hyperbolic space of dimension $n+1$ of a complete Riemannian manifold of dimension $n$ on which a compact connected group of intrinsic isometries acts with principal…

In this paper we describe a function $F_n:{\bf R}_+ \to {\bf R}_{+}$ such that for any hyperbolic n-manifold $M$ with totally geodesic boundary $\partial M \neq \emptyset$, the volume of $M$ is equal to the sum of the values of $F_n$ on the…

We compare the volume of a hyperbolic 3-manifold $M$ of finite volume and the complexity of its fundamental group.

We investigate the geometry of closed, orientable, hyperbolic $3$-manifolds whose fundamental groups are $k$-free for a given integer $k\ge 3$. We show that any such manifold $M$ contains a point $P$ of $M$ with the following property: If…

Under mild topological restrictions, we obtain new linear upper bounds for the dimension of the mod $p$ homology (for any prime $p$) of a finite-volume orientable hyperbolic $3$ manifold $M$ in terms of its volume. A surprising feature of…

Let n>2 and let M be an orientable complete finite volume hyperbolic n-manifold with (possibly empty) geodesic boundary having Riemannian volume vol(M) and simplicial volume ||M||. A celebrated result by Gromov and Thurston states that if M…

We give new information about the geometry of closed, orientable hyperbolic 3-manifolds with 4-free fundamental group. As an application we show that such a manifold has volume greater than 3.44. This is in turn used to show that if M is a…

If M is a compact oriented manifold-with-boundary whose fundamental group is virtually nilpotent or Gromov-hyperbolic, we show that the higher signatures of M are oriented-homotopy invariants.

We prove that given two compact oriented $3$-manifolds $N$ and $M,$ with $M$ satisfying only a mild hypothesis, there is a hyperbolic $3$-manifold $N'$ arbitrarily ``closely related'' to $N,$ and such that $N'$ does not embed in $M.$ For…

Suppose M is a connected, open, orientable, irreducible 3-manifold which is not homeomorphic to R^3. Given a compact 3-manifold J in M which satisfies certain conditions, Brin and Thickstun have associated to it an open neighborhood V$…

Assume that M is a closed hyperbolic 3-manifold fibering over the circle with fiber a closed orientable surface of genus g. We show that if M has large diameter and its injectivity radius is bounded below, then the rank of the fundamental…

We prove that if $(M, g)$ is a compact Riemannian manifold with ergodic geodesic flow, and if $H \subset M$ is a smooth hypersurface satisfying a generic asymmetry condition with respect to the geodesic flow, then restrictions $\phi_j |_H$…

Let $M_0$ be a compact and orientable 3-manifold. After capping off spherical boundaries with balls and removing any torus boundaries, we prove that the resulting manifold $M$ contains handlebodies of arbitrary genus such that the closure…

Let $M$ be a closed hyperbolic $3$-manifold. A homotopy class $[S]$ of surfaces in $M$ is filling if any representative cuts $M$ into components contractible in $M$. We prove that there exist $\epsilon_0, g_0>0$ such that every homotopy…

According to Mostow's celebrated rigidity theorem, the geometry of closed hyperbolic 3-manifolds is already determined by their topology. In particular, the volume of such manifolds is a topological invariant and, as such, has been…

We prove that on closed Riemannian manifolds with infinite abelian, but not cyclic, fundamental group, any isometry that is homotopic to the identity possesses infinitely many invariant geodesics. We conjecture that the result remains true…