The structure of limit groups over hyperbolic groups
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Wilton, HJR
Groves, D
Abstract
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.
Description
Keywords
math.GR, math.GR
Journal Title
Israel Journal of Mathematics
Conference Name
Journal ISSN
0021-2172
1565-8511
1565-8511
Volume Title
226
Publisher
Springer
Publisher DOI
Sponsorship
Engineering and Physical Sciences Research Council (EP/L026481/1)
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.