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

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

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arXiv · 1810.13285

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

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

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Abstract

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 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 $\mathbb{Z}^2$ subgroups.

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BibTeX RIS

Benjamin Beeker, Matthew Cordes, Giles Gardam, Radhika Gupta, Emily Stark. 2018-10-31. Cannon--Thurston maps for CAT(0) groups with isolated flats. https://arxiv.org/abs/1810.13285

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