This is the first in a series of papers dealing with the conjecture that. 11 compact 3-manifolds
admit canonical decompositions into geometric pieces. This conjecture will be discussed in …

By a hyperbolic 3-manifold we mean a complete orientable hyperbolic 3-manifold of finite …
Among hyperbolic 3-manifolds, the arithmetic ones form an interesting, and in many ways …

… a hyperbolic manifold is determined by its fundamental group. Theorem 3.1 says that any
invariant of the geometry of a hyperbolic manifold is … to the hyperbolic manifold. The method of …

0. Introduction This lecture gives an outline of basic geometric notions and ideas associated
with the conception of hyperbolicity. Very little is said here about the hyperbolic space itself (…

… manifold Mu is the n-fold cyclic covering of the three-dimensional sphere S 3 branched over
the figure-eight knot. We note that Mn are isometric to the hyperbolic manifolds … manifolds. …

… structure exists on Ō; by the Final Gluing Theorem applied to manifolds: Õ¡ is obtained by
gluing hyperbolic 3-manifolds Õ¡+1 along disjoint closed incompressible surfaces, where the …

… We now consider the general case in which M is a compact manifold containing r disjoint
two-sided embedded connected hypersurfaces Ml ,M2, ... ,Mr • We suppose we have a …

… In Section 5 we consider a class of rr-hyperbolic knots and their 2-fold branched coverings.
… 2-fold branched covering M of L give the torus decomposition of A4 into hyperbolic manifolds …

… related to hyperbolic fixed points and center manifolds. Then … of proof in the basic setting of
a hyperbolic fixed point. Then we … manifold (Q, g) as ambient space and a submanifold M. For …

… manifold fibered over the circle (see [15]). Namely, the Jorgensen group and our groups
have a form of a semidirect product of geometrically infinite normal subgroups and subgroups of …