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

Wise, Daniel T.

Canadian journal of mathematics, Tome 57 (2005) no. 2, pp. 416-448

Résumé

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.

Détail

DOI : 10.4153/CJM-2005-018-x

Mots-clés : 20F67, 20F06, CAT(0), periodic flat planes

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