Fundamental groups of 2-complexes with nonpositive planar sectional curvature

Abstract

We show that the finite simply connected 2-complexes of nonpositive planar sectional curvature are collapsible. Moreover, we show that each finite connected 2-complex with negative planar sectional curvature and fundamental group $\mathbb{Z}$ can be collapsed to a 1-dimensional cycle.

arXiv comment10 pages, 1 figure