Convergence groups are Fuchsian groups

David Gabai

doi:10.1090/S0273-0979-1991-16082-9

Convergence groups are Fuchsian groups

David Gabai

Research output: Contribution to journal › Comment/debate › peer-review

16 Scopus citations

Abstract

A group of homeomorphisms of the circle satisfying the “convergence property” is shown to be the restriction of a discrete group of Mobius transformations of the unit disk. This completes the proof of the Seifert fiber space conjecture and gives a new proof of the Nielson realization problem.

Original language	English (US)
Pages (from-to)	395-402
Number of pages	8
Journal	Bulletin of the American Mathematical Society
Volume	25
Issue number	2
DOIs	https://doi.org/10.1090/S0273-0979-1991-16082-9
State	Published - Oct 1991
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/S0273-0979-1991-16082-9

Cite this

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title = "Convergence groups are Fuchsian groups",

abstract = "A group of homeomorphisms of the circle satisfying the “convergence property” is shown to be the restriction of a discrete group of Mobius transformations of the unit disk. This completes the proof of the Seifert fiber space conjecture and gives a new proof of the Nielson realization problem.",

author = "David Gabai",

year = "1991",

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T1 - Convergence groups are Fuchsian groups

AU - Gabai, David

PY - 1991/10

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N2 - A group of homeomorphisms of the circle satisfying the “convergence property” is shown to be the restriction of a discrete group of Mobius transformations of the unit disk. This completes the proof of the Seifert fiber space conjecture and gives a new proof of the Nielson realization problem.

AB - A group of homeomorphisms of the circle satisfying the “convergence property” is shown to be the restriction of a discrete group of Mobius transformations of the unit disk. This completes the proof of the Seifert fiber space conjecture and gives a new proof of the Nielson realization problem.

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U2 - 10.1090/S0273-0979-1991-16082-9

DO - 10.1090/S0273-0979-1991-16082-9

M3 - Comment/debate

AN - SCOPUS:84967734548

SN - 0273-0979

VL - 25

SP - 395

EP - 402

JO - Bulletin of the American Mathematical Society

JF - Bulletin of the American Mathematical Society

IS - 2

ER -

Convergence groups are Fuchsian groups

Abstract

All Science Journal Classification (ASJC) codes

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