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

Published online by Cambridge University Press:  20 November 2018

Daniel T. Wise
Daniel T. Wise*
Affiliation:
Deptartment of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, QC, H3A 2K6, e-mail: wise@math.mcgill.ca
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Abstract

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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 $\mathcal{V}\mathcal{H}$-complexes. We solve the problem for malnormal and cyclonormal $\mathcal{V}\mathcal{H}$-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

20F6720F06CAT(0)periodic flat planes
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 57 , Issue 2 , 01 April 2005 , pp. 416 - 448
Copyright
Copyright © Canadian Mathematical Society 2005

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