TY - JOUR
T1 - Groups acting on hyperbolic-metric spaces
AU - Grecianu, Andrei Paul
AU - Kvaschuk, Alexei V.
AU - Myasnikov, Alexei G.
AU - Serbin, Denis E.
N1 - Publisher Copyright:
© 2015 World Scientific Publishing Company.
PY - 2015/9/1
Y1 - 2015/9/1
N2 - In this paper we study group actions on hyperbolic λ-metric spaces, where λ is an ordered abelian group. λ-metric spaces were first introduced by Morgan and Shalen in their study of hyperbolic structures and then Chiswell, following Gromov's ideas, introduced the notion of hyperbolicity for such spaces. Only the case of 0-hyperbolic λ-metric spaces (that is, λ-trees) was systematically studied, while the theory of general hyperbolic λ-metric spaces was not developed at all. Hence, one of the goals of the present paper was to fill this gap and translate basic notions and results from the theory of group actions on hyperbolic (in the usual sense) spaces to the case of λ-metric spaces for an arbitrary λ. The other goal was to show some principal difficulties which arise in this generalization and the ways to deal with them.
AB - In this paper we study group actions on hyperbolic λ-metric spaces, where λ is an ordered abelian group. λ-metric spaces were first introduced by Morgan and Shalen in their study of hyperbolic structures and then Chiswell, following Gromov's ideas, introduced the notion of hyperbolicity for such spaces. Only the case of 0-hyperbolic λ-metric spaces (that is, λ-trees) was systematically studied, while the theory of general hyperbolic λ-metric spaces was not developed at all. Hence, one of the goals of the present paper was to fill this gap and translate basic notions and results from the theory of group actions on hyperbolic (in the usual sense) spaces to the case of λ-metric spaces for an arbitrary λ. The other goal was to show some principal difficulties which arise in this generalization and the ways to deal with them.
KW - -hyperbolic group
KW - Hyperbolic group
KW - group action
KW - hyperbolic space
KW - λ-free group
UR - http://www.scopus.com/inward/record.url?scp=84942983728&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84942983728&partnerID=8YFLogxK
U2 - 10.1142/S0218196715500289
DO - 10.1142/S0218196715500289
M3 - Article
AN - SCOPUS:84942983728
SN - 0218-1967
VL - 25
SP - 977
EP - 1042
JO - International Journal of Algebra and Computation
JF - International Journal of Algebra and Computation
IS - 6
ER -