Cannon--Thurston maps for CAT(0) groups with isolated flats

Benjamin Beeker, Matthew Cordes, Giles Gardam, Radhika Gupta, Emily Stark

Published 2018-10-31Version 1

Mahan Mitra (Mj) proved Cannon--Thurston maps exist for normal hyperbolic subgroups of a hyperbolic group. We prove that Cannon--Thurston maps do not exist for infinite torsion-free normal hyperbolic subgroups of a non-hyperbolic CAT(0) group with isolated flats with respect to the visual boundaries. We also show Cannon--Thurston maps do not exist for infinite torsion-free infinite-index normal CAT(0) subgroups with isolated flats in a non-hyperbolic CAT(0) group with isolated flats. We determine the isomorphism types of the normal subgroups in the above two settings.