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- Title
Cannon–Thurston maps for CAT(0) groups with isolated flats.
- Authors
Benjamin, Beeker; Cordes, Matthew; Gardam, Giles; Gupta, Radhika; Stark, Emily
- Abstract
Mahan Mitra (Mj) proved Cannon–Thurston maps exist for normal hyperbolic subgroups of a hyperbolic group (Mitra in Topology, 37(3):527–538, 1998). We prove that Cannon–Thurston maps do not exist for infinite normal hyperbolic subgroups of non-hyperbolic CAT (0) groups with isolated flats with respect to the visual boundaries. We also show Cannon–Thurston maps do not exist for infinite infinite-index normal CAT (0) subgroups with isolated flats in non-hyperbolic CAT (0) groups with isolated flats. We obtain a structure theorem for the normal subgroups in these settings and show that outer automorphism groups of hyperbolic groups have no purely atoroidal Z 2 subgroups.
- Subjects
HYPERBOLIC groups
- Publication
Mathematische Annalen, 2022, Vol 384, Issue 1/2, p1
- ISSN
0025-5831
- Publication type
Article
- DOI
10.1007/s00208-021-02245-z