The boundary of the Gieseking tree in hyperbolic three-space
type: Item
instance of: scholarly article
title: The boundary of the Gieseking tree in hyperbolic three-space
zbMATH Open document ID: 0926.57008
DOI: 10.1016/S0166-8641(97)00270-8
author: Warren Dicks
author: Roger C. Alperin
author: Joan Porti
published in: Topology and its Applications
publication date: 1999-11-22T00:00:00Z
review text: In 1989, J. W. Cannon and W. P. Thurston proved that: Every lift to the universal cover of the embedding \(F \to M\) induces an embedding \({\mathbb H}^2 \to {\mathbb H}^3\) which extends continuously to a \(\pi _1(F)\)-equivariant quotient map \(\Psi : \partial {\mathbb H}^2 \to \partial {\mathbb H}^3\). In this paper, the authors give an elementary proof of the Cannon-Thurston theorem in the case of the Gieseking manifold, the three-manifold fibred over the circle \(S^1\) with fibre \(F\) a punctured torus, and with homological monodromy \(\left(\begin{smallmatrix} 0 & 1 \\ 1 &1 \end{smallmatrix}\right)\).
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 57M60
zbMATH DE Number: 1317213
zbMATH Keywords: Gieseking manifold
zbMATH Keywords: Cannon-Thurston map
zbMATH Keywords: ends of topological spaces
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1317213