Hyperbolization, Cubulation, and Applications in Negative Curvature Geometry

Explore the fascinating world of hyperbolization procedures in this 55-minute lecture by Lorenzo Ruffoni from Tufts University. Delve into the construction techniques that transform polyhedra into spaces of negative curvature while maintaining certain topological characteristics. Discover how these methods have been employed to create examples of manifolds with various pathologies, despite their negative curvature properties. Examine the unexpected relationship between these seemingly problematic manifolds and their fundamental groups, which exhibit surprisingly well-behaved properties. Learn about the joint work with J. Lafont, revealing that these groups allow for nice actions on CAT(0) cube complexes. Gain insights into new examples of negatively curved Riemannian manifolds whose fundamental groups are virtually special and algebraically fibered, showcasing the powerful applications of hyperbolization and cubulation techniques in geometric group theory and topology.