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Let G be a torsion-free hyperbolic group and let n ≥ 6 be an integer. We prove that G is the fundamental group of a closed aspherical manifold if the boundary of G is homeomorphic to an (n − 1)-dimensional sphere.doi:10.4310/jdg/1299766682 fatcat:m5buh2m5grdgnazn2ey2fdglmi