A gluing theorem for negatively curved complexes
arXiv:1510.02716 · doi:10.1112/jlms/jdw021
Abstract
A simplicial complex is called negatively curved if all its simplices are isometric to simplices in hyperbolic space, and it satisfies Gromov's Link Condition. We prove that, subject to certain conditions, a compact graph of spaces whose vertex spaces are negatively curved 2-complexes, and whose edge spaces are points or circles, is negatively curved. As a consequence, we deduce that certain groups are CAT(-1). These include hyperbolic limit groups, and hyperbolic groups whose JSJ components are fundamental groups of negatively curved 2-complexes---for example, finite graphs of free groups with cyclic edge groups.
26 pages. Typo corrected from previous version