Sectional curvature, compact cores, and local quasiconvexity (Q1889815)

The author defines the new notion of sectional curvature for 2-complexes as a generalization of curvature measure from the combinatorial Gauss-Bonnet theorem. The 2-complexes with nonpositive sectional curvature have coherent and locally indicable fundamental groups and they have the compact core property with finitely generated fundamental group. If a 2-complex with negative sectional curvature is a nonpositively curved Euclidian complex then its fundamental group is quasiconvex. The results are important because any finite volume cusped hyperbolic 3-manifold has a spine with nonpositive sectional curvature.