# Infinite group actions on spheres.

Revista Matemática Iberoamericana (1988)

- Volume: 4, Issue: 3-4, page 407-451
- ISSN: 0213-2230

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topMartin, Gaven J.. "Infinite group actions on spheres.." Revista Matemática Iberoamericana 4.3-4 (1988): 407-451. <http://eudml.org/doc/39367>.

@article{Martin1988,

abstract = {This paper is mainly intended as a survey of the recent work of a number of authors concerning certain infinite group actions on spheres and to raise some as yet unanswered questions. The main thrust of the current research in this area has been to decide what topological and geometrical properties characterise the infinite conformal or Möbius groups. One should then obtain reasonable topological or geometrical restrictions on a subgroup G of the homeomorphism group of a sphere which will imply that it can be made conformal after a change of coordinates. That is G is topologically conjugate to a Möbius group. Many aspects of the theory of Kleinian and Möbius groups can be found in the books [Ah 3], [Bea], [Mas 1], [MB] and Th].},

author = {Martin, Gaven J.},

journal = {Revista Matemática Iberoamericana},

keywords = {Acción de grupo; Grupos de Moebius; Esferas; Propiedades topológicas; conformal groups; quasiconformal groups; convergence groups; Möbius group acting on the n-sphere; survey; limit sets; Kleinian groups; group of homeomorphisms of ; 3-manifolds; 4-dimensional surgery; negatively curved manifolds; Teichmüller theory},

language = {eng},

number = {3-4},

pages = {407-451},

title = {Infinite group actions on spheres.},

url = {http://eudml.org/doc/39367},

volume = {4},

year = {1988},

}

TY - JOUR

AU - Martin, Gaven J.

TI - Infinite group actions on spheres.

JO - Revista Matemática Iberoamericana

PY - 1988

VL - 4

IS - 3-4

SP - 407

EP - 451

AB - This paper is mainly intended as a survey of the recent work of a number of authors concerning certain infinite group actions on spheres and to raise some as yet unanswered questions. The main thrust of the current research in this area has been to decide what topological and geometrical properties characterise the infinite conformal or Möbius groups. One should then obtain reasonable topological or geometrical restrictions on a subgroup G of the homeomorphism group of a sphere which will imply that it can be made conformal after a change of coordinates. That is G is topologically conjugate to a Möbius group. Many aspects of the theory of Kleinian and Möbius groups can be found in the books [Ah 3], [Bea], [Mas 1], [MB] and Th].

LA - eng

KW - Acción de grupo; Grupos de Moebius; Esferas; Propiedades topológicas; conformal groups; quasiconformal groups; convergence groups; Möbius group acting on the n-sphere; survey; limit sets; Kleinian groups; group of homeomorphisms of ; 3-manifolds; 4-dimensional surgery; negatively curved manifolds; Teichmüller theory

UR - http://eudml.org/doc/39367

ER -

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