Cannon–Thurston map
In mathematics, a Cannon–Thurston map is any of a number of continuous group-equivariant maps between the boundaries of two hyperbolic metric spaces extending a discrete isometric actions of the group on those spaces. The notion originated from a seminal 1980s preprint of James Cannon and William Thurston "Group-invariant Peano curves" (eventually published in 2007) about fibered hyperbolic 3-manifolds.