The boundary of the Gieseking tree in hyperbolic three-space

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• 作者：Alperin ; R.C. ; et. al.
• 关键词：Gieseking manifold ; Cannon&ndash ; Thurston map ; Ends of topological spaces
• 刊名：Topology and its Applications
• 出版年：1999
• 出版时间：May 25, 1999
• 年：1999
• 卷：93
• 期：3
• 页码：219-259
• 全文大小：541 K

文摘

We give an elementary proof of the Cannon–Thurston Theorem in the case of the Gieseking manifold. We do not use Thurston's structure theory for Kleinian groups but simply calculate with two-by-two complex matrices. 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.