Strict hyperbolization of flat manifolds Charney–Davis strict hyperbolization is a construction that takes a nonpositively curved cubulated manifold (or cube complex) and turns it into a negatively curved space. In this talk, I will discuss two extra features of strict hyperbolization. First, it can be carried out in a way that preserves the stable tangent bundle of the input manifold. Second, when applied to a suitable class of flat manifolds, it produces closed hyperbolic manifolds with interesting topological properties. Applications include new examples of closed hyperbolic manifolds with nontrivial Pontryagin and Stiefel–Whitney classes, hyperbolic manifolds that occur as totally geodesic boundaries of other hyperbolic manifolds, and aspherical topological manifolds with hyperbolic fundamental group that admit no smooth structure. This is joint work with Eduardo Reyes and Stefano Riolo.

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Last modified: Mon Mar 16 14:50:16 EDT 2026