The structure of limit groups over hyperbolic groups
Israel Journal of Mathematics
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Wilton, H., & Groves, D. (2018). The structure of limit groups over hyperbolic groups. Israel Journal of Mathematics, 226 119-176. https://doi.org/10.1007/s11856-018-1692-2
fundamental case in which Γ is free, may not be finitely presentable or geometrically tractable. We define model Γ-limit groups, which always have good geometric properties (in particular, they are always relatively hyperbolic). Given a strict resolution of an arbitrary Γ-limit group L, we canonically construct a strict resolution of a model Γ-limit group, which encodes all homomorphisms L → Γ that factor through the given resolution. We propose this as the correct framework in which to study Γ-limit groups algorithmically. We enumerate all Γ-limit groups in this framework.
The work of the first author was supported by the National Science Foundation and by a grant from the Simons Foundation (#342049 to Daniel Groves). The second author was supported by the EPSRC.
External DOI: https://doi.org/10.1007/s11856-018-1692-2
This record's URL: https://www.repository.cam.ac.uk/handle/1810/265722