Hyperbolic Manifolds in Dimension Higher Than 3

Explore the intricacies of hyperbolic manifolds in dimensions higher than 3 in this comprehensive conference talk. Delve into the fundamental concept of hyperbolic manifolds as Riemannian manifolds with constant sectional curvature -1. Learn about the abundance of compact hyperbolic manifolds in dimensions n≥2 and their crucial role in the topology of surfaces and 3-manifolds. Discover the challenges in describing concrete examples in dimensions ≥4 and gain insights into the current state of knowledge regarding hyperbolic manifolds in higher dimensions. This talk provides a thorough review of the subject, offering valuable information for mathematicians and researchers interested in topology and geometry.