Details of Grant 

EPSRC Reference:	GR/K25618/01
Title:	ENDS OF PAIRS OF GROUPS,AND GROUPS ACTING ON CUBE COMPLEXES
Principal Investigator:	Dunwoody, Professor M
Other Investigators:	Bowditch, Professor B Niblo, Professor GA
Researcher Co-Investigators:
Project Partners:
Department:	School of Mathematics
Organisation:	University of Southampton
Scheme:	Standard Research (Pre-FEC)
Starts:	01 September 1995	Ends:	30 November 1998	Value (£):	115,567
EPSRC Research Topic Classifications:	Algebra & Geometry
EPSRC Industrial Sector Classifications:
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Panel History:
Summary on Grant Application Form
We will generalise the Bass-Serre theory for discrete groups by studying group actions on finite dimensional, non-positively curved cube complexes. We will relate this work to the generalisations of Stallings splitting theory introduced by Dunwoody, Kropholler and Roller.Non-positively curved cube complexes form a class of CAT (0) spaces which seem particularly amenable to enquiry, and we will investigate their geometry. In particular we will study the geometry of flat sub-spaces they contain, in order to illuminate conjectures of Gromov et al about the existence of abelian subgroups in their fundamental groups. This will entail introducing a notion of flat measured lamination for a cube complex, developing surgery techniques for these objects and applying Rips ideas to approximate a group action on the lamination by a group action on a tree.
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Organisation Website:	http://www.soton.ac.uk