Combinatorial negative curvature and triangulations of 3-manifolds Damian Osajda 20F6757M50combinatorial nonpositive curvaturethree manifoldhyperbolic group We introduce and study local combinatorial conditions on a simplicial complex, implying Gromov hyperbolicity of its universal cover. We apply the theory to Thurston's problem on $5/6^{*}$-triangulations of $3$-manifolds, providing a new proof and generalizing the original result. We indicate further applications. Indiana University Mathematics Journal 2015 text pdf 10.1512/iumj.2015.64.5568 10.1512/iumj.2015.64.5568 en Indiana Univ. Math. J. 64 (2015) 943 - 956 state-of-the-art mathematics http://iumj.org/access/