Finite Group Actions on 3-Manifolds and Nielsen Realization

Explore finite group actions on 3-manifolds and their connection to Nielsen realization in this 52-minute conference talk by Bena Tshishiku from Brown University, presented at the Fields Institute's Algebraic Topology Interactions conference. Delve into the mathematical framework governing how finite groups can act on three-dimensional manifolds, examining the theoretical foundations and practical implications of these actions. Investigate the Nielsen realization problem, which addresses when a group homomorphism can be realized by a homeomorphism, and discover how this classical problem in topology intersects with the study of 3-manifold geometry. Learn about the sophisticated techniques used to analyze these group actions, including methods from algebraic topology, geometric topology, and group theory. Gain insights into current research developments in this area of mathematics and understand how finite group actions provide a powerful tool for studying the structure and classification of 3-manifolds.