A combination theorem for strong relative hyperbolicity

Mj, Mahan; Reeves, Lawrence

doi:10.2140/gt.2008.12.1777

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A combination theorem for strong relative hyperbolicity

Mahan Mj and Lawrence Reeves

Geometry & Topology 12 (2008) 1777–1798

DOI: 10.2140/gt.2008.12.1777

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

Volume 12, issue 3 (2008)