The boundary of the Gieseking tree in hyperbolic three-space

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

doi:10.1016/S0166-8641(97)00270-8

The boundary of the Gieseking tree in hyperbolic three-space

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

Departament de Matemàtiques

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Resum

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.

Idioma original	Anglès
Pàgines (de-a)	219-259
Revista	Topology and its Applications
Volum	93
Número	3
DOIs	https://doi.org/10.1016/S0166-8641(97)00270-8
Estat de la publicació	Publicada - 1 de des. 1999

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10.1016/S0166-8641(97)00270-8

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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. {\textcopyright} 1999 Elsevier Science B.V. All rights reserved.",

keywords = "Cannon-Thurston map, Ends of topological spaces, Gieseking manifold",

author = "Alperin, \{R. C.\} and Warren Dicks and J. Porti",

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AU - Alperin, R. C.

AU - Dicks, Warren

AU - Porti, J.

PY - 1999/12/1

Y1 - 1999/12/1

N2 - 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.

AB - 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.

KW - Cannon-Thurston map

KW - Ends of topological spaces

KW - Gieseking manifold

UR - https://www.scopus.com/pages/publications/0009362511

U2 - 10.1016/S0166-8641(97)00270-8

DO - 10.1016/S0166-8641(97)00270-8

M3 - Article

SN - 0016-660X

VL - 93

SP - 219

EP - 259

JO - Topology and its Applications

JF - Topology and its Applications

IS - 3

ER -

The boundary of the Gieseking tree in hyperbolic three-space

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