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Distortion of surface groups in CAT(0) free-by-cyclic groups. (English) Zbl 1167.20024
Summary: Given a non-positively curved 2-complex with a circle-valued Morse function satisfying some extra combinatorial conditions, we describe how to locally isometrically embed this in a larger non-positively curved 2-complex with free-by-cyclic fundamental group. This embedding procedure is used to produce examples of CAT(0) free-by-cyclic groups that contain closed hyperbolic surface subgroups with polynomial distortion of arbitrary degree. We also produce examples of CAT(0) hyperbolic free-by-cyclic groups that contain closed hyperbolic surface subgroups that are exponentially distorted.

20F65 Geometric group theory
20F67 Hyperbolic groups and nonpositively curved groups
57M20 Two-dimensional complexes (manifolds) (MSC2010)
Full Text: DOI
[1] Bestvina M., Brady N. (1997). Morse theory and finiteness properties of groups. Invent. Math. 129(3):445–470 · Zbl 0888.20021
[2] Brady, N., Crisp, J.: CAT(0) and CAT() dimensions of torsion free hyperbolic groups. Preprint (2005) · Zbl 1145.20023
[3] Brady, N., Forester, M., Shankar, K.: Dehn functions of subgroups of CAT(0) groups. Preprint (2005)
[4] Bridson, M.R.,Haefliger,A.: Metric spaces of Non-Positive Curvature, Grundle. Math.Wisse., vol. 319, Springer-Verlag, Berlin (1999) · Zbl 0988.53001
[5] Howie, J.:On the asphericity of ribbon disc complements. Trans. Amer.Math. Soc. 289(1), 281–302(1985) · Zbl 0572.57001
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