Fundamental groups of 2-complexes with nonpositive planar sectional curvature

Lycka Drakengren

Published 2024-01-07Version 1

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.