Approximating Flats by Periodic Flats in CAT(0) Square Complexes
Daniel T. Wise · Canadian Journal of Mathematics · 2005
Abstract We investigate the problem of whether every immersed flat plane in a nonpositively curved square complex is the limit of periodic flat planes. Using a branched cover, we reduce the problem to the case of VH-complexes. We solve the problem for malnormal and cyclonormal VH-complexes. We also solve the problem for complete square complexes using a different approach. We give an application towards deciding whether the elements of fundamental groups of the spaces we study have commuting powers. We note a connection between the flat approximation problem and subgroup separability.