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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
 

Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 126, Number 3, March 1998, Pages 877880
S 0002-9939(98)04458-X
SIMPLE QUOTIENTS OF HYPERBOLIC 3-MANIFOLD GROUPS
D. D. LONG AND A. W. REID
(Communicated by James West)
Abstract. We show that hyperbolic 3-manifolds have residually simple fun-
damental group.
1. Introduction
Let G be a finitely generated group and X a property of groups, e.g. finite,
simple, p-group. G is said to be residually X, if for any element g = 1, there is a
group H with property X and a surjective homomorphism : G H such that
(g) = 1.
Of interest to us are residual properties of groups 1(M) where M is a compact
orientable 3-manifold with infinite fundamental group. Now it is well-known that
if M is a hyperbolic 3-manifold, that is the quotient of hyperbolic 3-space by a
torsion-free Kleinian group, then 1(M) is residually finite. In this note we prove
a much stronger result which seems to have been unnoticed previously. First we
make a definition.

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara
Reid, Alan - Department of Mathematics, University of Texas at Austin

 

Collections: Mathematics