Conformally non-spherical 2-complexes (Q1323462)

Conformally non-spherical 2-complexes are 2-complexes which are non- positively curved in a combinatorial sense. Included among these complexes are the non-positively curved (metric), piecewise euclidean 2- complexes introduced by Gersten and Stallings. It is shown that a finite cyclic group acting on a conformally non-spherical 2-complex has a fixed point. This yields a classification of the torsion in certain generalized small cancellation groups and the fundamental groups of certain complexes of groups. Also it is shown that finite, conformally hyperbolic 2- complexes have fundamental groups that are word hyperbolic in the sense of Gromov.