Homology Cobordism and the Geometry of Hyperbolic Three-Manifolds

Explore the intricate relationship between hyperbolic geometry and homology cobordism in this conference talk from the Gauge Theory and Low Dimensional Topology event. Delve into the challenges of understanding the three-dimensional homology cobordism group structure as Francesco Lin from Columbia University presents his research. Learn how monopole Floer homology serves as a powerful tool for investigating fundamental properties of subgroups within the homology cobordism group, specifically those generated by hyperbolic homology spheres under certain geometric constraints. Gain insights into this complex area of mathematics and its implications for low-dimensional topology and gauge theory.