Sectional curvature, compact cores, and local quasiconvexity

Abstract

We define a new notion of sectional curvature for 2-complexes, and describe a variety of examples with nonpositive or negative sectional curvature. The 2-complexes with nonpositive sectional curvature have coherent and locally indicable fundamental groups. The 2-complexes with negative sectional curvature have the compact core property for covers with finitely generated fundamental group. The fundamental groups of compact 2-complexes with metric negative sectional curvature have locally-quasiconvex fundamental groups.