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# Approximating Flats by Periodic Flats in \\CAT(0) Square Complexes

Published:2005-04-01
Printed: Apr 2005
• Daniel T. Wise
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## 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 $\V$-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
 MSC Classifications: 20F67 - Hyperbolic groups and nonpositively curved groups 20F06 - Cancellation theory; application of van Kampen diagrams [See also 57M05]

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