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.
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Wise, D. Sectional curvature, compact cores, and local quasiconvexity. Geom. funct. anal. 14, 433–468 (2004). https://doi.org/10.1007/s00039-004-0463-x
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DOI: https://doi.org/10.1007/s00039-004-0463-x