A Kieinian group with contractible quotient not simply connected at infinity
نویسندگان
چکیده
We give an example of a co-compact Kleinian group F which contains a subgroup F 0 having the property that E~/Fo is contractible but not simply connected at infinity.
منابع مشابه
Coxeter Groups and Asphericalmanifolds
I. Contractible manifolds and aspherical manifolds. Suppose that M n is a compact, contractible n-manifold with boundary. These assumptions imply that the boundary of M has the homology of an (n-l)-sphere; however, they do not imply that it is simply connected. If n ~ 3, then for M n to be homeomorphic to a disk it is obviously necessary that ~M be simply connected. For n ~ 5 this condition is ...
متن کاملObservations on Lickorish Knotting of Contractible 4–manifolds
Lickorish has constructed large families of contractible 4–manifolds that have knotted embeddings in the 4–sphere and has also shown that every finitely presented perfect group with balanced presentation occurs as the fundamental group of the complement of a knotted contractible manifold. Here we make a few observations regarding Lickorish’s construction, showing how to extend it to construct c...
متن کاملHomotopy of Ends and Boundaries of CAT(0) Groups
For n ≥ 0, we exhibit CAT(0) groups that are n-connected at infinity, and have boundary which is (n− 1)-connected, but this boundary has non-trivial n-homotopy group. In particular, we construct 1ended CAT(0) groups that are simply connected at infinity, but have a boundary with non-trivial fundamental group. Our base examples are 1-ended CAT(0) groups that have non-path connected boundaries. I...
متن کاملA Proof of Uniqueness of the Taub-bolt Instanton
We show that the Riemannian Schwarzschild and the “Taub-bolt” instanton solutions are the only spaces (M, gμν) such that • M is a 4-dimensional, simply connected manifold with a Riemannian, Ricci-flat C2−metric gμν which admits (at least) a 1-parameter group μτ of isometries without isolated fixed points on M. • The quotient (M\LM)/μτ (where LM is the set of fixed points of μτ ) is an asymptoti...
متن کاملSome results of semilocally simply connected property
If we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. In this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.
متن کامل