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Un Groupe Hyperbolique Est Déterminé Par Son Bord
Author(s) -
Paulin Frédéric
Publication year - 1996
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/54.1.50
Subject(s) - bijection, injection and surjection , group (periodic table) , boundary (topology) , mathematics , measure (data warehouse) , pure mathematics , construct (python library) , combinatorics , mathematical analysis , computer science , physics , data mining , quantum mechanics , programming language , bijection
We construct on the boundary of a hyperbolic group (in Gromov's sense) a natural visual measure and a natural crossratio. We prove that the I‐quasiconformal homeomorphisms (in Pansu's sense) between the boundaries of hyperbolic groups are the quasimöbius maps (that is, the bijections that almost preserve the crossratios), and that they are the extensions of the quasi‐isometries between the groups. We define a barycentre for every probability measure on the boundary without atom, extending the Douady‐Earle construction.