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Title:
Hyperbolic groups, Cannon-Thurston maps, and hydra
Speaker:
Abstract:
Groups are Gromov-hyperbolic when all geodesic triangles in their Cayley graphs are close to being tripods. Despite being tree-like in this manner, they can harbour extreme wildness in their subgroups. I will describe examples stemming from a re-imagining of Hercules' battle with the hydra, where wildness is found in properties of "Cannon-Thurston maps" between boundaries. Also, I will give examples where this map between boundaries fails to be defined. This is joint work with O. Baker.
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