Abstract
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.
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References
Bestvina M., Brady N. (1997). Morse theory and finiteness properties of groups. Invent. Math. 129(3):445–470
Brady, N., Crisp, J.: CAT(0) and CAT(−1) dimensions of torsion free hyperbolic groups. Preprint (2005)
Brady, N., Forester, M., Shankar, K.: Dehn functions of subgroups of CAT(0) groups. Preprint (2005)
Bridson, M.R.,Haefliger,A.: Metric spaces of Non-Positive Curvature, Grundle. Math.Wisse., vol. 319, Springer-Verlag, Berlin (1999)
Howie, J.:On the asphericity of ribbon disc complements. Trans. Amer.Math. Soc. 289(1), 281–302(1985)
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Barnard, J., Brady, N. Distortion of Surface Groups in CAT(0) free-by-cyclic Groups. Geom Dedicata 120, 119–139 (2006). https://doi.org/10.1007/s10711-006-9072-1
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DOI: https://doi.org/10.1007/s10711-006-9072-1