Some applications of ℓ_p-cohomology to boundaries of Gromov hyperbolic spaces

We study quasi-isometry invariants of Gromov hyperbolic spaces, focusing on the ℓ_p -cohomology and closely related invariants such as the conformal dimension, combinatorial modulus, and the Combinatorial Loewner Property. We give new constructions of continuous ℓ_p-cohomology, thereby obtaining information about the ℓ_p-equivalence relation, as well as critical exponents associated with ℓ_p-cohomology. As an application, we provide a flexible construction of hyperbolic groups which do not have the Combinatorial Loewner Property, extending [8] and complementing the examples from [10]. Another consequence is the existence of hyperbolic groups with Sierpinski carpet boundary which have conformal dimension arbitrarily close to 1. In particular, we answer questions of Mario Bonk, Juha Heinonen and John Mackay.