Homology cobordism and the geometry of hyperbolic three-manifolds

Francesco Lin (Columbia)

Abstract: A major challenge in the study of the structure of the three-dimensional homology cobordism group is to understand the interaction between hyperbolic geometry and homology cobordism. In this talk, I will discuss how monopole Floer homology can be used to study some basic properties of certain subgroups of the homology cobordism group generated by hyperbolic homology spheres satisfying some natural geometric constraints.