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THE BOUNDARY OF THE GIESEKING TREE IN HYPERBOLIC THREE-SPACE
 

Summary: THE BOUNDARY OF THE GIESEKING
TREE IN HYPERBOLIC THREE-SPACE
R. C. Alperin*, W. Dicks**, J. Porti**
Abstract. We give an elementary proof of the Cannon-Thurston Theorem in
the case of the Gieseking manifold. We work entirely on the boundary, using
ends of trees, and obtain pictures of the regions which are successively filled in
by the Peano curve of Cannon and Thurston.
1. Introduction
The Gieseking manifold M is the three-manifold fibered over the circle S1
with fibre F a punctured torus, and with homological monodromy 0 1
1 1
.
This monodromy determines the manifold M, which is unorientable, and hy-
perbolic, with an unoriented cusp.
Let Hn
denote n-dimensional hyperbolic space. Its boundary, Hn
, is
homeomorphic to the (n-1)-sphere Sn-1
, and its compactification, Hn
Hn

  

Source: Alperin, Roger C. - Department of Mathematics, San Jose State University

 

Collections: Mathematics