The boundary of the Gieseking tree in hyperbolic three-space

R. C. Alperin, Warren Dicks, J. Porti

Research output: Contribution to journalArticleResearchpeer-review

13 Citations (Scopus)

Abstract

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. © 1999 Elsevier Science B.V. All rights reserved.
Original languageEnglish
Pages (from-to)219-259
JournalTopology and its Applications
Volume93
Issue number3
Publication statusPublished - 1 Dec 1999

Keywords

  • Cannon-Thurston map
  • Ends of topological spaces
  • Gieseking manifold

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