Scott and Swarup’s regular neighborhood as a tree of cylinders

Vincent Guirardel and Gilbert Levitt

Vol. 245 (2010), No. 1, 79–98

DOI: 10.2140/pjm.2010.245.79

Abstract

Let G be a finitely presented group. Scott and Swarup have constructed a canonical splitting of G that encloses all almost invariant sets over virtually polycyclic subgroups of a given length. We give an alternative construction of this regular neighborhood by showing that it is the tree of cylinders of a JSJ splitting.

Keywords

JSJ decomposition, tree of cylinder, almost invariant set, torus theorem, canonical splitting, tree

Mathematical Subject Classification 2000

Primary: 20E08

Secondary: 20F65, 20E06

Milestones

Received: 9 December 2008

Accepted: 1 September 2009

Published: 20 January 2010