On the Deleted Squares of Lens Spaces
Explore a 58-minute lecture on the topology of configuration spaces in lens spaces. Delve into the concept of deleted squares of manifolds and their homotopy properties. Learn about the groundbreaking examples by Longoni and Salvatore that demonstrate how homotopy equivalent lens spaces can have non-homotopy equivalent deleted squares. Investigate the relationship between homeomorphic 3-dimensional lens spaces and the homotopy equivalence of their deleted squares. Discover the advanced mathematical tools employed in this study, including Cheeger-Simons differential characters and Massey products of universal covers. Gain insights from the joint work of Nikolai Saveliev and Kyle Evans-Lee as they explore this fascinating area of algebraic topology.