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 $\V$-complexes. We solve the problem for malnormal and cyclonormal $\V$-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.

Keywords:

CAT(0), periodic flat planes CAT(0), periodic flat planes

MSC Classifications:

20F67, 20F06 show english descriptions Hyperbolic groups and nonpositively curved groups
Cancellation theory; application of van Kampen diagrams [See also 57M05] 20F67 - Hyperbolic groups and nonpositively curved groups
20F06 - Cancellation theory; application of van Kampen diagrams [See also 57M05]

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