The boundary of the Gieseking tree in hyperbolic three-space
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 \(\left(\begin{smallmatrix} 0 & 1 \\ 1 &1 \end{smallmatrix}\right)\).
scientific article; zbMATH DE number 1317213