Bridging the Gap Between Homology Planes and Mazur Manifolds

Explore the fascinating connection between homology planes and Mazur manifolds in this 42-minute conference talk. Delve into the concept of Kirby-Ramanujam spheres, which are homology 3-spheres that bound both a homology plane and a Mazur type manifold. Discover several infinite families of these unique spheres and related topics as presented by Rodolfo Aguilar from the University of Miami. Gain insights into the interplay between complex surfaces and 4-manifolds, first observed by C. P. Ramanujam and R. Kirby. Learn about homology planes as algebraic complex smooth surfaces with integral homology groups identical to the complex plane, and Mazur type manifolds as compact contractible smooth 4-manifolds constructed using only 0-, 1-, and 2-handles. Understand the collaborative research efforts behind this presentation, conducted jointly with Oğuz Şavk.