×

zbMATH — the first resource for mathematics

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.

MSC:
20F65 Geometric group theory
20F67 Hyperbolic groups and nonpositively curved groups
57M20 Two-dimensional complexes (manifolds) (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.