Volume 12, issue 3 (2008)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A combination theorem for strong relative hyperbolicity

Mahan Mj and Lawrence Reeves

Geometry & Topology 12 (2008) 1777–1798
Abstract

We prove a combination theorem for trees of (strongly) relatively hyperbolic spaces and finite graphs of (strongly) relatively hyperbolic groups. This gives a geometric extension of Bestvina and Feighn’s Combination Theorem for hyperbolic groups and answers a question of Swarup. We also prove a converse to the main Combination Theorem.

Keywords
relative hyperbolicity, tree, hyperbolic metric space
Mathematical Subject Classification 2000
Primary: 20F67
Secondary: 57M50
References
Publication
Received: 30 March 2007
Revised: 10 April 2008
Accepted: 21 May 2008
Published: 4 July 2008
Proposed: Benson Farb
Seconded: Walter Neumann, Dave Gabai
Authors
Mahan Mj
RKM Vivekananda University
Belur Math
WB-711 202
India
Lawrence Reeves
University of Melbourne
Victoria 3010
Australia